Question

The volume of a right circular cone is 9856 cm^3If
the diameter of the base of cone is 28 cm, find
the height of cone
slant height of cone
curved surface area of the cone.​

Answer 1

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Answer 2

$\huge{\underline{\sf{\orange{Solution-}}}}$

${\underline{\sf{\orange{Given-}}}}$

$\sf{Volume = 9856 {cm}^{3}}$

$\sf{diameter\:of\:base = 28cm}$

$\sf{radius = 14 cm}$

${\underline{\sf{\orange{Find-}}}}$

i) Height of the cone.

ii) Slant Height of the cone.

iii) Curved surface area.

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1. Height of the cone = h

Volume of the cone $\huge{\underline{\sf{\orange{= \dfrac{1}{3}\pi{r}^{2}h-}}}}$

$\longrightarrow \sf {\dfrac{ 1}{3} \pi {r}^{2}h = 9856}$

$\longrightarrow \sf{ \dfrac{ 1}{3}\times \dfrac{22}{7} \times {14}^{2} \times h = 9856}$

$\longrightarrow \sf {\dfrac{1 }{3} \times \dfrac{22}{7} \times 14 \times 14 \times h = 9856}$

$\longrightarrow \sf {\dfrac{616}{3}\times h = 9856}$

$\longrightarrow \sf{h = \dfrac{9856 \times 3}{616}}$

$\longrightarrow \sf{h = 16 \times 3}$

$\longrightarrow \sf\orange{h = 48 cm}$

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2. Slant height of the cone = ?

$\longrightarrow\huge \sf\orange{{l}^{2} = {h}^{2}+ {r}^{2}}$

$\longrightarrow \sf{{l}^{2} = {48}^{2}+ {14}^{2}}$

$\longrightarrow \sf{{l}^{2} = 2304+ 196}$

$\longrightarrow\sf{{l}^{2} = 2500}$

$\longrightarrow\sf{l = \sqrt{2500}}$

$\longrightarrow\sf\orange{l = 50cm}$

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3. Curved surface area of the cone $\huge\sf\orange{\pi rl}$

$\longrightarrow\sf {\dfrac{22}{7}\times 14 \times 50}$

$\longrightarrow\sf{44 \times 50}$

$\longrightarrow\sf\orange{= 2200{cm}^{2}}$

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