# Mathematics Questions and Answers – Volume of a Right Circular Cone

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Volume of a Right Circular Cone”.

1. Volume of a right circular cone of radius r and height h is given by __________
a) $$\frac{4}{3} πr^3$$
b) πr2h
c) $$\frac{1}{3}$$ πr2h
d) $$\frac{2}{3}$$ πr3

Explanation: Volume of three cones is equal to volume of a cylinder which has the same radius and height as the cone.
We know that volume of a cylinder = πr2h
Hence, volume of a cone = $$\frac{1}{3}$$ πr2h.

2. What is the volume of a cone having radius of 21cm and height of 5cm?
a) 2310cm3
b) 2500cm3
c) 6930cm3
d) 7500cm3

Explanation: We know that volume of a cone = $$\frac{1}{3}$$ πr2h
= $$\frac{1}{3} * \frac{22}{7}$$ * 21 * 21 * 5
= 6930cm3.

3. A cone has slanted height of 5cm and height of 4cm, its volume (in cm3) is __________
a) 38.71
b) 36.50
c) 37.00
d) 37.71

Explanation: From the figure shown below, According to Pythagoras theorem, r2 + h2 = l2
r = $$\sqrt{l^2-h^2}$$
= $$\sqrt{5^2-4^2}$$
= 3cm
We know that volume of a cone = $$\frac{1}{3}$$ πr2h
= $$\frac{1}{3} * \frac{22}{7}$$ * 3 * 3 * 4
= 37.71.
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4. Ratio of volume of a cone to the volume of a cylinder for same base radius and same height is __________
a) 3
b) $$\frac{1}{3}$$
c) 2
d) $$\frac{1}{2}$$

Explanation: We know that volume of a cone = $$\frac{1}{3}$$ πr2h and volume of a cylinder= πr2h
Hence, $$\frac{volume \,of \,a \,cone}{volume \,of \,a \,cylinder} = \frac{1/3 πr^2 h}{πr^2 h}$$
= $$\frac{1}{3}$$.

5. A triangle having sides equal to 7cm, 24cm and 25cm forms a cone when revolved about 24cm side. What is the volume of a cone formed?
a) 1225cm3
b) 1232cm3
c) 4000cm3
d) 3696cm3

Explanation: As shown in the figure, when the cone is formed, its base radius is 14cm and height is 24cm. We know that volume of a cone = $$\frac{1}{3}$$ πr2h
= $$\frac{1}{3} * \frac{22}{7}$$ * 7 * 7 * 24
= 1232cm3.

Sanfoundry Global Education & Learning Series – Mathematics – Class 9.

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