Question

The volume of a come is 1570 cm^3 . if its base aria is 314 cm^3,then its height is:-​

Answer 1

$\huge{\red{\underline{\underline{\rm{Answer:-}}}}}$

$\star{\blue{\underline{\bf{Given:-}}}}$

${\green{\tt{\implies Volume\;of\;cone=1570\;cm^{3}}}}$

${\green{\tt{\implies Base\;area\;of\;cone\;(\pi r^{2})=314\;cm^{2}}}}$

$\star{\blue{\underline{\bf{To\;Find:-}}}}$

${\green{\tt{\implies Height\;of\;the\;cone.}}}$

$\star{\blue{\underline{\bf{Formula\;used:-}}}}$

$\star{\boxed{\green{\tt{Volume\;of\;cone=\dfrac{1}{3} \pi r^{2} h}}}}$

${\green{\textsf{Now, put the values in the formula, we get,}}}$

${\green{\tt{\implies Volume\;of\;cone=\dfrac{1}{3}\pi r^{2}h}}}$

${\green{\tt{\implies 1570=\dfrac{1}{3}\times 314\times h}}}$

${\green{\tt{\implies h=\dfrac{1570\times 3}{314}}}}$

${\green{\tt{\implies h=\dfrac{4710}{314}}}}$

${\green{\tt{\implies h=15}}}$

${\purple{\underline{\underline{\bf{\therefore Height\;of\;the\;cone=15\;cm}}}}}$

Answer 2

Question :-

The volume of a come is 1570 cm^3 . if its base aria is 314 cm^3,then its height is:-

Answer :-

→ Height (h) of cone is 15 cm.

To find :-

→ Height of cone

Formula used :-

$\star \boxed{ \red{\boxed{ \sf{ \red{volume \: of \: cone \: } = \green{\frac{1}{3} \pi \: {r}^{2} h}}}}}$

Step - by - step explanation :-

According to the question,

$\rightarrow \sf{ \blue{volume \: of \: cone} \: = 1570 \: {cm}^{3} } \\ \\ \rightarrow \: \sf{ \red{ base \: area \: of \: cone} \: ( \pi \: {r}^{2} ) = \green{ 314 { \: cm}^{2}} } \\ \\ \rm{ apply \: the \: given \: formula \: } \\ \\ \pink{\rightarrow} \sf{ 1570 = \red {\frac{1}{3} ( \pi \: {r}^{2} )h}} \\ \\ \blue{\rightarrow} \sf{ \green{1570 }= \blue{ \frac{1}{3} \times 314 \times h}} \\ \\ \green{\rightarrow }\sf{ h = \red{ \frac{4710}{314} } }\\ \\ \red{\rightarrow} \boxed{ \sf{ h \: = \blue{ 15}}}$

Therefore height of cone is 15 cm.

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