Question

The height of right circular cone is 12cm^2.If its volume is 100πr^3.Find its slant height.

Answer 1

hope it helps you..................

Answer 2

$\large\underline\pink{Given:-}$

• Volume of circular cone = 100π cm³.
• Height of circular cone = 12cm.

$\large\underline\pink{To find:-}$

• Fine the slant height ....?

$\large\underline\pink{Solutions:-}$

• $\: \: \: \: \: Volume \: \: of \: \: cone \: \: = \: \: \frac{1}{3} \: \pi \: {r}^{2} \: h$

$\: \: \: \: \: \leadsto \: \: {100} \pi \: \: = \: \: \frac{1}{3} \pi \: \times \: {r}^{2} \: \times \: {12}$

$\: \: \: \: \: \leadsto \: \: {100} \pi \: \: = \: \: \frac{12}{3} \pi \: \times \: {r}^{2}$

$\: \: \: \: \: \leadsto \: \: {100} \pi \: \: = \: \: {4} \pi \: \times \: {r}^{2}$

$\: \: \: \: \: \leadsto \: \: \frac{{100} \pi}{{4} \pi} \: \: = \: \: {r}^{2}$

$\: \: \: \: \: \leadsto \: \: {25} \: \: = \: \: {r}^{2}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: {\sqrt{25}}$

$\: \: \: \: \: \leadsto \: \: {r} \: \: = \: \: {5}$

Now, So the slant height by using the pythagoras theorem.

⟹ l² = r² + h²

⟹ l² = (5)² + (12)²

⟹ l² = 25 + 144

⟹ l² = 169

⟹ l = √169

⟹ l = 13

Hence, the slant height is 13 cm.

Right circular cone:-

• h = height of cone
• r = Radius of cone
• s = slant height

• Volume = 1/3πr²h
• Lateral surface area = πr √r²+h²
• Total surface area = πr² + πr √r²+h²