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) πr^{2}h

c) \(\frac{1}{3}\) πr^{2}h

d) \(\frac{2}{3}\) πr^{3}

View Answer

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 = πr

^{2}h

Hence, volume of a cone = \(\frac{1}{3}\) πr

^{2}h.

2. What is the volume of a cone having radius of 21cm and height of 5cm?

a) 2310cm^{3}

b) 2500cm^{3}

c) 6930cm^{3}

d) 7500cm^{3}

View Answer

Explanation: We know that volume of a cone = \(\frac{1}{3}\) πr

^{2}h

= \(\frac{1}{3} * \frac{22}{7}\) * 21 * 21 * 5

= 6930cm

^{3}.

3. A cone has slanted height of 5cm and height of 4cm, its volume (in cm^{3}) is __________

a) 38.71

b) 36.50

c) 37.00

d) 37.71

View Answer

Explanation: From the figure shown below,

According to Pythagoras theorem, r

^{2}+ h

^{2}= l

^{2}

r = \(\sqrt{l^2-h^2}\)

= \(\sqrt{5^2-4^2}\)

= 3cm

We know that volume of a cone = \(\frac{1}{3}\) πr

^{2}h

= \(\frac{1}{3} * \frac{22}{7}\) * 3 * 3 * 4

= 37.71.

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) \(\frac{1}{2}\)

View Answer

Explanation: We know that volume of a cone = \(\frac{1}{3}\) πr

^{2}h and volume of a cylinder= πr

^{2}h

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) 1225cm^{3}

b) 1232cm^{3}

c) 4000cm^{3}

d) 3696cm^{3}

View Answer

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 = \(\frac{1}{3}\) πr

^{2}h

= \(\frac{1}{3} * \frac{22}{7}\) * 7 * 7 * 24

= 1232cm

^{3}.

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

To practice all areas of Mathematics, __ here is complete set of 1000+ Multiple Choice Questions and Answers__.

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