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

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 2

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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Previous Year Stats

Solids - Volume

1

question from CAT exam over the past 5 years

Formulas Asked Together in Previous Papers


Surface Area of Solids

1 PYQ

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