Question

volume of the cone is 288Pi cm3 and radius is 6cm .then find the height​

Answer 1

Given:

• volume of the cone =288pi cm³
• Radius =6cm

To find out:

Height =?

Formula used:

$volume \: of \: cone = \pi \: r {}^{2} \frac{h}{3}$

Solutions:

$288\pi \: cm { }^{2} = \pi \times 6 {}^{2} \times \frac{h}{3}$

$288\pi \times 3 = 36\pi \: h$

$864\pi = 36\pi \: h$

$h = \frac{864\pi}{36\pi}$

$h = \red {24 \: cm}$

Answer 2

Given :

• Volume of cone → 288 π cm³
• Radius of cone → 6 cm.

To Find :

• Height of the cone

Solution :

- Volume of cone is ⅓ volume of a cylinder.

- Volume of cone equals as ⅓ times value of π times value of square of radius times the height of the cone.

Formula :

$\large{\boxed{\sf{\red{Volume_{cone}\:=\:\dfrac{1}{3}\:\pi\:r^2h}}}}$

Where,

• Volume → 288 π cm³
• r → radius = 6 cm
• h → height of cone

Block in the available data,

$\longrightarrow$ $\sf{288\:\pi\:=\:\dfrac{1}{\cancel{3}}\:\:\times\:\pi\:\times\:\cancel{6}\:\times\:6\:\times\:h}$

$\longrightarrow$ $\sf{288\:\pi\:=\:\pi\:\times\:2\:\times\:6\:\times\:h}$

$\longrightarrow$ $\sf{288\:\pi\:=\:\:12\:\pi\:h}$

$\longrightarrow$ $\sf{\dfrac{288\:\cancel{ \pi}}{12\:\cancel{\pi}}\:=\:h}$

$\longrightarrow$ $\sf{\cancel{\dfrac{288}{12}}\:=\:h}$

$\longrightarrow$ $\sf{24=h}$

$\large{\boxed{\sf{\purple{Height\:of\:the\:cone\:=\:24\:cm}}}}$