Question : The slant height and radius of a right circular cone are in the ratio 29 : 20. If its volume is $4838.4 π {cm}^{3}$ , then its radius is:
Option 1: 28 cm
Option 2: 20 cm
Option 3: 25 cm
Option 4: 24 cm

Question

Question : The ratio of the height and the diameter of a right circular cone is 6: 5 and its volume is $\frac{2200}{7} {cm}^{3}$ . What is its slant height?
(Take $π = \frac{22}{7}$ )
Option 1: 26 cm
Option 2: 13 cm
Option 3: 25 cm
Option 4: 5 cm

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Answer 1

Correct Answer: 24 cm

Solution : The ratio of slant height and radius = 29 : 20
Let slant height( $l$ ) be $29 x$ and radius( $r$ ) be $20 x$ .
Height, $h = \sqrt{l^{2} - r^{2}} = \sqrt{(29 x)^{2} - (20 x)^{2}} = \sqrt{(841 - 400) x^{2}} = \sqrt{441 x^{2}} = 21 x$
Volume of cone = $4838.4 π$
⇒ $\frac{1}{3} π r^{2} h = 4838.4 π$
⇒ $\frac{1}{3} \times π \times (20 x)^{2} \times 21 x = 4838.4 π$
⇒ $x^{3} = \frac{4838.4 \times 3}{400 \times 21} = \frac{172.8}{100} = 1.728$
⇒ $x = \sqrt[3]{1.728} = 1.2$
Radius = $20 x = 20 \times 1.2 = 24$ cm
Hence, the correct answer is 24 cm.

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Question : The slant height and radius of a right circular cone are in the ratio 29 : 20. If its volume is 4838.4π cm3, then its radius is:Option 1: 28 cmOption 2: 20 cmOption 3: 25 cmOption 4: 24 cm

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Question : The slant height and radius of a right circular cone are in the ratio 29 : 20. If its volume is $4838.4 π {cm}^{3}$ , then its radius is:
Option 1: 28 cm
Option 2: 20 cm
Option 3: 25 cm
Option 4: 24 cm