Question

The slant height of a cone is 14 m and its curved surface is 264 m2 . Find the radius of the base of a cone.​

Answer 1

Answer:

Given :-

• The slant height of a cone is 14 m and its curved surface area is 264 m².

To Find :-

• What is the radius of the base of a cone.

Formula Used :-

$\clubsuit$ Curved Surface Area or CSA of Cone Formula :

$\mapsto \sf\boxed{\bold{\pink{C.S.A_{(Cone)} =\: {\pi}rl}}}$

where,

• C.S.A = Curved Surface Area
• π = pie or 22/7
• r = Radius
• l = Slant Height

Solution :-

Given :

• Slant Height (l) = 14 m
• Curved Surface Area (C.S.A) = 264 m²

According to the question by using the formula we get,

$\longrightarrow \sf \dfrac{22}{\cancel{7}} \times r \times {\cancel{14}} =\: 264$

$\longrightarrow \sf 22 \times r \times 2 =\: 264$

$\longrightarrow \sf r =\: \dfrac{264}{22 \times 2}$

$\longrightarrow \sf r =\: \dfrac{\cancel{264}}{\cancel{44}}$

$\longrightarrow \sf r =\: \dfrac{6}{1}$

$\longrightarrow \sf\bold{\red{r =\: 6\: m}}$

${\small{\bold{\underline{\therefore\: The\: radius\: of\: the\: base\: of\: a\: cone\: is\: 6\: m\: .}}}}$

Answer 2

$\huge \sf {\underbrace{\underline{Elucidation:-}}}$

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$\rm \red {\underline{\underline{Provided\: that:}}}$

➻The slant height of a cone(l)=14m

➻Curved surface area of the cone(C.S.A)=264${m^{2}}$

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$\rm \blue {\underline{\underline{To\: be\: Determined:}}}$

➻ Radius of the base of a cone(r)=?

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$\rm \pink {\underline{\underline{We\: know:}}}$

$\tiny \tt \green {\fbox{Curved\:surface\:area\:of\:a\:cone(C.S.A)=πrl}}$

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➻We've been given curved surface area (C.S.A) and slant height (l).

➻Supplanting those values in the formula,

$\colon \mapsto \tt{C.S.A=πrl}$

$\large \colon \mapsto \tt {264m^{2}=\frac{22}{7}\times r\times 14m }$

$\large \colon \mapsto \tt {r=\frac{264m^{2}\times{\cancel{ 7}}}{22\times {\cancel{14}}m_{2} }}$

$\large \colon \mapsto \tt {r=\frac{264m^{2}}{22\times 2m }}$

$\large \colon \mapsto \tt {r=\frac{\cancel{264m^{2}}^{6}}{\cancel{44m} }}$

$\colon \implies \green {\fbox{r=6m}}$

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$\rm \purple {\underline{\underline{Thereupon,}}}$

➻Radius of the base of a cone(r)=6m

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