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
View Answer

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

Answer: a
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
View Answer

Answer: d
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) \(\frac{1}{2}\)
View Answer

Answer: b
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
View Answer

Answer: b
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.
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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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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter