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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)

πr2h

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

$$\dfrac{1}{3}$$π 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)

$$\dfrac{4}{3}$$πr3

Solid Hemisphere (radius r)

$$\dfrac{2}{3}$$πr3


Hollow Hemisphere (radius r)

$$\dfrac{2}{3}$$πr3


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?

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