# Recent questions tagged mensuration

1

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...

2

3

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 ...

4

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...

5

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...

6

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 $9$ ...

7

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...

8

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 ...

9

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...

10

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...

11

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...

12

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

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...

14

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...

15

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...

16

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...

17

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...

18

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...

19

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 ...

20

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...

21

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...

22

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...

23

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...