Question

The height and the slant height of a cone is 21 cm and 28 cm respectively. find the volume of cone.​

Answer 1

$\underline\mathfrak\blue{ᴀɴsᴡᴇʀ:-}$

$~~~~~\fbox\gray{7546\:cm³}$

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$\underline\mathfrak\blue{ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ:-}$

$From \: l {}^{2} \: = r {}^{2} + h {}^{2} \\ \\ we \: have, \: r \: = \: \sqrt{l {}^{2} - h {}^{2} } = \sqrt{28 {}^{2} - 21 {}^{2} } \: cm \: = 7 \sqrt{7} cm \\ \\ \\ So, \: volume \: of \: the \: cone \: = \: \dfrac{1}{3} \pi r {}^{2} h \: = \: \dfrac{1}{3} \times \dfrac{22}{7} \times 7 \sqrt{7} \times 7 \sqrt{7} \times 21 \: cm {}^{2} \\ \\ = \: 7546 \: cm {}^{3}$

Answer 2

Answer:

Given height of cone = h = 21 cm and slant height = 28 cm.

As h²+ r² = ĺ² => 21²+r² = 28²

=> r² = 28² - 21² =343 => r= 7root7 cm.

Volume of cone = 1/3pier²h = 1/3×22/7×(7root7)²×21cm³= 7546 cm³