Question

The height and slant height of a cone are 21cm and 28cm respectively, find its volume.

Answer 1

By Pythagoras theorem,
(slant height)² = (radius )² + ( height)²
⇒radius² = (28)² - (21)²
               = (28 +21) (28- 21)
               = 49 × 7
radius = 7√7 cm
now, volume = ( π r² h)/3
                     =((22/7)× 343× 21)/3
                     = 7546 cm³
∴ volume = 7546 cm³

Answer 2

Hi there !

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Height of the cone ( h ) = 21 cm.

Slant height ( l ) = 28 cm.

From l² = b² + h², we have ;

⇒ r = √ l² - h²

⇒ r = √ 28² - 21²

⇒ r = √ 784 - 441

⇒ r = √ 343

⇒r = 7 √ 7 cm.

So,

Volume of cone = $\mathsf {\frac {1} {3}}$ π r² h

$⇒ \mathsf{\frac{1}{3} \times \frac{22}{7} \times 7 \sqrt{7} \times 7 \sqrt{7} \times 21 } \\ \\ ⇒ \mathsf{22 \times 49 \times 7} \\ \\ ⇒ \mathsf{7546 \: cm {}^{3} }$

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Thanks for the question!

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