Recent questions tagged mensuration

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CAT 2003 | Question: 2-65
Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of $n$ turns (in other words, the ... drawn to scale). How is $h$ related to $n?$ $h=\sqrt{2}n$ $h=\sqrt{17}n$ $h=n$ $h=\sqrt{13}n$

Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylind...

Lakshman Bhaiya

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Lakshman Bhaiya asked Mar 31, 2022

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CAT 2003 | Question: 2-64
Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of $n$ turns (in other ... , not drawn to scale). The length of the string, in cms, is $\sqrt{2}n$ $\sqrt{12}n$ $n$ $\sqrt{13}n$

Consider a cylinder of height $h$ cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylind...

Lakshman Bhaiya

13.7k points

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Lakshman Bhaiya asked Mar 31, 2022

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1 answer

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CAT 2020 Set-1 | Question: 76
A solid right circular cone of height $27$ cm is cut into two pieces along a plane parallel to its base at a height of $18$ cm from the base. If the difference in volume of the two pieces is $225$ cc, the volume, in cc, of the original cone is $232$ $256$ $264$ $243$

A solid right circular cone of height $27$ cm is cut into two pieces along a plane parallel to its base at a height of $18$ cm from the base. If the difference in volume ...

soujanyareddy13

2.7k points

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soujanyareddy13 asked Sep 16, 2021

1 votes

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CAT 2019 Set-2 | Question: 92
A man makes complete use of $405$ cc of iron, $783$ cc of aluminium, and $351$ cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius $3$ cm. If the total number ... the total surface area of all these cylinders, in sq cm, is $8464\pi$ $928\pi$ $1044(4+\pi)$ $1026(1+\pi)$

A man makes complete use of $405$ cc of iron, $783$ cc of aluminium, and $351$ cc of copper to make a number of solid right circular cylinders of each type of metal. Thes...

13.9k points

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go_editor asked Mar 20, 2020

2 votes

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CAT 2019 Set-2 | Question: 94
The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being $20$ cm. The vertical height of the pyramid, in cm, is $8\sqrt{3}$ $12$ $5\sqrt{5}$ $10\sqrt{2}$

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being $20$ cm. The vertical height of the pyram...

13.9k points

535 views

go_editor asked Mar 20, 2020

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CAT 2018 Set-1 | Question: 81
A right circular cone, of height $12$ ft, stands on its base which has diameter $8$ ft. The tip of the cone is cut off with a plane which is parallel to the base and $9$ ft from the base. With $\pi = 22/7$, the volume, in cubic ft, of the remaining part of the cone is ________

A right circular cone, of height $12$ ft, stands on its base which has diameter $8$ ft. The tip of the cone is cut off with a plane which is parallel to the base and $9$ ...

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606 views

go_editor asked Mar 19, 2020

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CAT 2017 Set-1 | Question: 84
A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio $1: 1:8: 27: 27$. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to $10$ $50$ $60$ $20$

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio $1: 1:8: 27: 27$. The percentage by which the sum of the surface areas of these fi...

13.9k points

534 views

go_editor asked Mar 13, 2020

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1 answer

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CAT 2017 Set-1 | Question: 85
A ball of diameter $4$ cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is $3$ cm, while its volume is $9\pi \;\text{cm}^{3}$. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is $5$ $4$ $3$ $6$

A ball of diameter $4$ cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is $3$ cm, while its volume is $9\pi \;\text{cm}^{3}$. Then ...

13.9k points

510 views

go_editor asked Mar 13, 2020

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CAT 2016 | Question: 68
A cube of side $12\; \text{cm}$ is painted red on all the faces and then cut into smaller cubes, each of side $3 \text{cm}$. What is the total number of smaller cubes having none of their faces painted _________

A cube of side $12\; \text{cm}$ is painted red on all the faces and then cut into smaller cubes, each of side $3 \text{cm}$. What is the total number of smaller cubes hav...

13.9k points

519 views

go_editor asked Mar 11, 2020

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CAT 2016 | Question: 72
A wooden box (open at the top) of thickness $0.5\:\text{cm}$, length $21\:\text{cm}$, width $11\:\text{cm}$ and height $6\:\text{cm}$ is painted on the inside. The expenses of painting are Rs. $70$. What is the rate of painting per square centimetres? $\text{Re}\;0.7$ $\text{Re}\;0.5$ $\text{Re}\;0.1$ $\text{Re}\;0.2$

A wooden box (open at the top) of thickness $0.5\:\text{cm}$, length $21\:\text{cm}$, width $11\:\text{cm}$ and height $6\:\text{cm}$ is painted on the inside. The expens...

13.9k points

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go_editor asked Mar 11, 2020

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CAT 2015 | Question: 74
A wooden box (open at the top) of thickness $0.5$ cm, length $21$ cm, width $11$ cm and height $6$ cm is painted on the inside. The expenses of painting are $\text{Rs. 70}$. What is the rate of painting per square centimeters? $\text{Re 0.7}$ $\text{Re 0.5}$ $\text{Re 0.1}$ $\text{Re 0.2}$

A wooden box (open at the top) of thickness $0.5$ cm, length $21$ cm, width $11$ cm and height $6$ cm is painted on the inside. The expenses of painting are $\text{Rs. 70...

13.9k points

401 views

go_editor asked Mar 9, 2020

2 votes

1 answer

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CAT 2019 Set-1 | Question: 94
If the rectangular faces of a brick have their diagonals in the ratio $3:2\sqrt{3}:\sqrt{15}$, then the ratio of the length of the shortest edge of the brick to that of its longest edge is $\sqrt{3}:2$ $2:\sqrt{5}$ $1:\sqrt{3}$ $\sqrt{2}:\sqrt{3}$

If the rectangular faces of a brick have their diagonals in the ratio $3:2\sqrt{3}:\sqrt{15}$, then the ratio of the length of the shortest edge of the brick to that of i...

13.9k points

614 views

go_editor asked Mar 8, 2020

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CAT 2013 | Question: 14
A cuboidal aquarium, of base dimensions $100\;\text{cm} \times 80\;\text{cm}$ and height $60\;\text{cm}$, is filled with water to its brim. The aquarium is now tilted along one of the $80\;\text{cm}$ edges and the water begin to spill. The ... . Now the box is returned to its original position. By how many centimeters has the height of water reduced? $50$ $40$ $20$ $10$

A cuboidal aquarium, of base dimensions $100\;\text{cm} \times 80\;\text{cm}$ and height $60\;\text{cm}$, is filled with water to its brim. The aquarium is now tilted alo...

4.5k points

848 views

admin asked Mar 6, 2020

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CAT 2012 | Question: 24
A solid sphere of radius $12$ inches and cast into a right circular cone whose base diameter is $\sqrt{2}$times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out? $4$ and $1$ cubic inch $3$ and $12$ cubic inches $4$ and $0$ cubic inch $3$ and $6$ cubic inches

A solid sphere of radius $12$ inches and cast into a right circular cone whose base diameter is $\sqrt{2}$times its slant height. If the radius of the sphere and the cone...

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Chandanachandu asked Mar 5, 2020

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CAT 2003 | Question: 2-63
Consider a cylinder of height h cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns ( ... consecutive turns? $\frac{h}{n}$ $\frac{h}{\sqrt{n}}$ $\frac{h}{n^2}$ Cannot be determined with given information

Consider a cylinder of height h cms and radius $r=\frac{2}{\pi}$ cms as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindri...

13.9k points

682 views

go_editor asked May 4, 2016

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16

CAT 2000 | Question: 109
Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds $500$ litres more than the conical tank. After $200$ litres of fuel has been pumped out from each tank the cylindrical tank contains twice the ... conical tank. How many litres of fuel did the cylindrical tank have when it was full? $700$ $1000$ $1100$ $1200$

Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds $500$ litres more than the conical tank. After $200$ li...

13.9k points

545 views

go_editor asked Mar 30, 2016

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CAT 2003 | Question: 1-138
There are $8436$ steel balls, each with a radius of $1$ centimeter, stacked in a pile, with $1$ ball on top, $3$ balls in second layer, $6$ in the third layer, $10$ in the fourth, and so on. The number of horizontal layers in the pile is $34$ $38$ $36$ $32$

There are $8436$ steel balls, each with a radius of $1$ centimeter, stacked in a pile, with $1$ ball on top, $3$ balls in second layer, $6$ in the third layer, $10$ in th...

13.9k points

408 views

go_editor asked Feb 9, 2016

1 votes

1 answer

18

CAT 2003 | Question: 1-107
Let $\text{A}$ and $\text{B}$ two solid spheres such that the surface area of $\text{B}$ is $300\%$ higher than the surface area of $\text{A}.$ The volume of $\text{A}$ is found to be $k\%$ lower than the volume of $\text{B}.$ The value of $k$ must be ________ $85.5$ $92.5$ $90.5$ $87.5$

Let $\text{A}$ and $\text{B}$ two solid spheres such that the surface area of $\text{B}$ is $300\%$ higher than the surface area of $\text{A}.$ The volume of $\text{A}$ i...

13.9k points

571 views

go_editor asked Feb 5, 2016

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19

CAT 2014 | Question: 37
A lead cuboid of $8$ inches in length, $11$ inches in breadth, and $2$ inches thick was melted and resolidified into the form of a rod of $8$ inches diameter. The length of such a rod, in inches, is nearest to $3$ $3.5$ $4$ $4.5$

A lead cuboid of $8$ inches in length, $11$ inches in breadth, and $2$ inches thick was melted and resolidified into the form of a rod of $8$ inches diameter. The length ...

8.1k points

563 views

makhdoom ghaya asked Jan 17, 2016

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20

CAT 2014 | Question: 26
Three identical cones with base radius $r$ are placed on their bases so that each is touching the other two. The radius of the circle drawn through their vertices is smaller than $r$. equal to $r$. larger than $r$. depends on the height of the cones.

Three identical cones with base radius $r$ are placed on their bases so that each is touching the other two. The radius of the circle drawn through their vertices is smal...

8.1k points

617 views

makhdoom ghaya asked Jan 16, 2016

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2 answers

21

CAT 2004 | Question: 72
If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be equal to the sides of the cube $\sqrt{3}$ times the sides of the cube $\frac{1} {\sqrt{3} }$ times the sides of the cube impossible to find from the given information

If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribi...

13.9k points

1.5k views

go_editor asked Jan 14, 2016

1 votes

1 answer

22

CAT 2006 | Question: 54
The length, breadth and height of a room are in the ration $3:2:1.$ If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will remain the same. decrease by $13.64\%$ decrease by $15\%$ decrease by $18.75\%$ decrease by $30\%$

The length, breadth and height of a room are in the ration $3:2:1.$ If the breadth and height are halved while the length is doubled, then the total area of the four wall...

13.9k points

867 views

go_editor asked Dec 28, 2015

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CAT 2008 | Question: 05
Consider a right circular cone of base radius $4$ cm and height $10$ cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq cm) of the cylinder. $\frac{100 \pi}{3}$ $\frac{80 \pi}{3}$ $\frac{120 \pi}{7}$ $\frac{130 \pi}{9}$ $\frac{110 \pi}{7}$

Consider a right circular cone of base radius $4$ cm and height $10$ cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of t...

13.9k points

651 views

go_editor asked Nov 28, 2015

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