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Recent questions tagged mensuration

1 1 vote
1 1 answer
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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 cylind...
0 0 votes
1 answers 1 answer
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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 cylind...
4 4 votes
1 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 ...
1 1 vote
1 1 answer
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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. Thes...
2 2 votes
1 1 answer
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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 pyram...
2 2 votes
1 1 answer
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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 $9$ ...
4 4 votes
1 1 answer
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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 fi...
1 1 vote
1 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 ...
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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 hav...
0 0 votes
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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 expens...
0 0 votes
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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...
2 2 votes
1 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 i...
0 0 votes
1 1 answer
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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 alo...
0 0 votes
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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...
0 0 votes
0 0 answers
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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 cylindri...
0 0 votes
0 0 answers
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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 $200$ li...
0 0 votes
0 0 answers
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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 th...
2 2 votes
1 answers 1 answer
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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 $\text{A}$ i...
0 0 votes
0 0 answers
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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 ...
0 0 votes
0 0 answers
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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 smal...
0 0 votes
2 2 answers
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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 circumscribi...
1 1 vote
1 1 answer
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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 wall...
0 0 votes
1 1 answer
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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 t...
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