Question

The volume of the cone is 462m3 . its base radius is 7m. find the height

Answer 1

Answer:

9 m.

Step-by-step explanation:

Given:

Volume of cone = 462 m³

Base radius = 7 m

We know that,

$volume \: of \: a \: cube \: = \pi {r}^{2} \frac{h}{3} \\ \\ \frac{22}{7} \times {(7)}^{2} \times \frac{h}{3} = 462 \\ \\ \frac{22}{7} \times 49 \times \frac{h}{3} = 462 \\ \\ \frac{22 \times 49 \times h}{21} = 462 \\ \\ 1078h = 9702 \\ \\ h = \frac{9702}{1078} \\ \\ h \: = 9$

Therefore, the height of the cone is 9 m.

Answer 2

Answer: Height = 9m

Solution:

$\bold{\underline{\sf{\red{\:\:Given:-\:\:}}}}$

The volume of a cone is 462m³

We know that,

Formula of cone:

$:\implies\large{\underline{\boxed{\sf{\pink{\dfrac{1}{3} \: \pi \: r^2 h }}}}}$

$:\implies\sf\: \dfrac{1}{3} \times \: \dfrac{22}{7} \times \: 7^2 \times \: h = 462$

$:\implies\sf\: \dfrac{1}{3} \times \: 22 \times \: 7 \times \: h = 462$

$:\implies\sf\: 154 \times \: h = 1386$

$:\implies\sf\: h = \dfrac{1386}{154}$

$:\implies\large{\underline{\boxed{\sf{\blue{Height\:=\: 9 \: m }}}}}$

$\bold{\underline{\sf{\blue{Hence\: The\: Height\: of \: the \: cone \: is \: 9 \; m}}}}$