Question

Volume of cone is 288πcm³ and radius is 6cm then find it's height​

Answer 1

Given :-

volume = 288πcm³

Radius = 6cm

Solution :-

Volume of cone is 1/3 cylinder's volume

Volume of cone = 1/3 πr²h

• volume = 288πcm³
• radius (r) = 6cm
• h (height)

➡ 288 π = 1/3 × π × 6 × 6 × h

➡ 288 π = π × 2 × 6 × h

➡ 288 π = 12 π h

➡ 288 π/12 π = h

➡ 288/12 = h

➡ h = 24

.°. Height of the cone = 24 cm.

Answer 2

AnsWer :

24 Cm.

Given :

• Volume of Cone is 288π³
• Radius of cone is 6 Cm.

Formula :

$\tt \dagger \: \: \: \: \: V_{Cone} = \frac{1}{3}\pi {r}^{2} h$

$\tt \dagger \: \: \: \: \: TSA_{Cone} = \pi r( r + l )$

$\tt \dagger \: \: \: \: \: CSA_{Cone} = \pi rl$

$\tt \dagger \: \: \: \: \: Slant \: Height_{Cone} ( l ) = \sqrt{ {r}^{2} + {h}^{2} }$

To Find :

• Height of Cone.

Solution :

$\tt \longmapsto V_{Cone} = \frac{1}{3}\pi {r}^{2} h$

$\tt \longmapsto 288 \pi= \frac{1}{3}\pi {r}^{2} h$

$\tt\longmapsto 288 = \frac{1}{3} {r}^{2} h$

$\tt\longmapsto 288 \times 3= {(6)}^{2} \times h$

$\tt\longmapsto \dfrac{288 \times 3}{36} = h$

$\tt\longmapsto \dfrac{288}{12} = h$

$\tt\longmapsto h = 24 \: cm.$

Therefore, the height of Cone is 24 Cm.