Question

The base area of cone is 38.5 and volume is 77 then find height?

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Height\:of\:cone=6\:cm}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a cone whose base area and volume is given.

• We have to find the height of cone.

$\underline \bold{Given : } \\ \implies Base \: Area \: of \: cone = 38.5 \: {cm}^{2} \\ \\ \implies Volume \: of \: cone = 77 {cm}^{3} \\ \\ \underline \bold{to \: find :} \\ \implies Height \: of \: cone = ?$

• According to given question :

$\bold{Formula \: Area \: of \:circle : } \\ \implies \pi {r}^{2} = 38.5 \\ \\ \bold{\implies {r}^{2} = \frac{38.5}{\pi}} \\ \\ \bold{By \: Formula \: of \: Volume \: of \: cone : } \\ \implies \frac{1}{3} \pi {r}^{2} h = 77 \\ \\ \bold{Putting \: value \: of \: {r}^{2} } \\ \implies \frac{1}{3} \times \frac{ \cancel{22}}{ \cancel{7}} \times \frac{ 38.5 \times \cancel7}{ \cancel{22}} \times h = 77 \\ \\ \implies \frac{ {38.5}}{ 3} \times h = 77 \\ \\ \implies h = \frac{ 77 \times 3}{ 38.5} \\ \\ \implies h = \frac{ \cancel{231}}{ \cancel{38.5}} \\ \\ \bold{\implies h = 6 \: cm} \\ \\ \bold{\therefore Height \: of \: cone \: is \: 6 \: cm}$