A conical vessel has radius 4 cm, and its curved surface area is 20π cm². Find the volume of conical vessel?

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RRB NTPC Exam 20 Jan 2021 click here to view all questions

A conical vessel has radius 4 cm, and its curved surface area is 20π cm². Find the volume of conical vessel?

A16π cm³

B14π cm³

C26π cm³

D64π/3 cm³

Akhilesh ? Apr 12 '25 at 08:10

correct answer is: option d) 64π/3 cm³
Explanation: The curved surface area of a cone is given by \(πrl\),

where \(r\) is the radius and \(l\) is the slant height.

We are given that the radius \(r = 4\) cm and the curved surface area is \(20π\) cm².

Therefore, we have \(π(4)l = 20π\), which implies \(l = 5\) cm.

The height \(h\) of the cone can be found using the Pythagorean theorem: \(h^2 + r^2 = l^2\), so \(h^2 + 4^2 = 5^2\),

which means \(h^2 = 25 - 16 = 9\).

Thus, \(h = 3\) cm. The volume of the cone is given by \(\frac{1}{3}πr^2h\). Substituting the values \(r = 4\) and \(h = 3\),

we get \(V = \frac{1}{3}π(4^2)(3) = \frac{1}{3}π(16)(3) = 16π\) cm³

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correct answer is: option d) 64π/3 cm³ Explanation: The curved surface area of a cone is given by \(πrl\), where \(r\) is the radius and \(l\) is the slant height. We are given that the radius \(r = 4\) cm and the curved surface area is \(20π\) cm². Therefore, we have \(π(4)l = 20π\), which implies \(l = 5\) cm. The height \(h\) of the cone can be found using the Pythagorean theorem: \(h^2 + r^2 = l^2\), so \(h^2 + 4^2 = 5^2\), which means \(h^2 = 25 - 16 = 9\). Thus, \(h = 3\) cm. The volume of the cone is given by \(\frac{1}{3}πr^2h\). Substituting the values \(r = 4\) and \(h = 3\), we get \(V = \frac{1}{3}π(4^2)(3) = \frac{1}{3}π(16)(3) = 16π\) cm³ Akhilesh ? answered Apr 12 '25 at 08:10

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