Question

The Height and the slant Height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone​

Answer 1

Answer:

7546cm³

Step-by-step explanation:

h=21 cm

l= 28 cm

since a cone forms a right angle triangle

therfore;

h²=p²+b² (Pythagoras theroem)

28²= 21²+ b²(b= radius of the cone)

b²= 784 - 441

b= √343

vol. = πr²h/3

= π √343×√343× 21/3

= 22×343×21/21

= 22×343

=7546 cm³

Answer 2

☘️ Given :

• Height = 21 cm
• Slant height (length) = 28 cm
• Find the volume of the cone.

☘️ Solution :

We know that,

Volume of the cone = 1/3 πr²h

To find base radius 'r' we use the relation between r, l and h.

We know that in a cone,

$\\ \purple{ \bf\: ➝ \: \: l² = r² + h² } \\ \sf \: ➝ \:r = \sqrt{l {}^{2} - h {}^{2} } \\ \sf \: ➝ \:r = \sqrt{28 {}^{2} - 21 {}^{2} } \: cm \\ \sf \: ➝ \:r = 7 \sqrt{7} \: cm \\ \\ \: \: \: \: \: \: \underline{\boxed{ \therefore \: \rm\purple{ r= 7 \sqrt{7} \: cm }}}$

So, volume of the cone

$\large \rm \purple{ = \: \: \dfrac{1}{3}\pi \: r {}^{2}h } \ \\ \\ = \: \sf\frac{1}{3} \times \frac{22}{7} \times 7 \sqrt{7} \times 7 \sqrt{7} \times 21 \: cm {}^{3} \\ = \: \sf22 \times 7 \sqrt{7} \times 7 \sqrt{ 7} \: cm {}^{3} \\ = \sf \: 22 \times 7 \times 7 \times ( \sqrt{7} ) {}^{2} \: cm {}^{3} \\ = \sf \: 22 \times 7 \times 7 \times 7 \: cm {}^{3} \\ = \sf \: 7546 \: cm {}^{3} \\ \\ \underline {\boxed{ \pink{\therefore \: \rm the \: volume \: of \: the \: cone \: = \: 7546 \: cm {}^{3} } \: }}$