Solids - Volume

Rarely Tested

TYPE OF SOLIDVOLUME

Cube (all sides equal to a)

a3

Cuboid (length l, breadth b, height h)

lbh

Right Circular Cylinder (radius r, height h)

Ο€r2h

Right Circular Cone (radius r, height h, slant height l)

$$\dfrac{1}{3}$$Ο€ r2h

Cone frustum (radii $$r_1$$, $$r_2$$, height h and slant height l)$$V=\dfrac{1}{3}\pi h(r_2^2+r_1r_2+r_1^2)$$

Sphere (radius r)

$$\dfrac{4}{3}$$Ο€r3

Solid Hemisphere (radius r)

$$\dfrac{2}{3}$$Ο€r3


Hollow Hemisphere (radius r)

$$\dfrac{2}{3}$$Ο€r3


Pyramid$$\dfrac{1}{3}\times\ Area\ of\ the\ base\times\ Height$$

Prism$$Base\ Area\times\ Height$$

Volume of Tetrahedron of side 'a' = $$\dfrac{a^3}{6\sqrt{\ 2}}$$

Formula Video


Question 1

The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is

Question 2

A cube is dropped into water and is then cut into 64 small cubes. How many of these smaller cubes are wet on exactly two of their sides?

Question 3

A cube of side 20 cm is painted yellow and is cut into smaller cubes of side 5 cm each. What is the number of cubes with no side painted yellow?

Log in to view all questions

Go back to topics

Join CAT 2026 course by 5-Time CAT 100%iler

Crack CAT 2026 & Other Exams with Cracku!