Question

a cone of a diameter 42 centimetre asmoli 12935 cm cube
find its slant height and curved surface area

Answer 1

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the area of cone is given 12935 cm³ , it has diameter of 42 cm so, r = d/2 =42/2 =21.

we know the formula of cone
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink{ \huge \frac{1}{3} \pi {r}^{2} h}$
π = 22/7 (given)

$12935 = \frac{1}{3 } \times \frac{22}{7} \times (21 )^{2} \times h \\ \\ 12935 = \frac{1}{ \cancel{3 \: } } \times \frac{22}{7} \times \cancel{21} ^{ \: \: 7} \times 21 \times h \\ \\ 12935 = 462 \times h \\ \\ \: h = \frac{12935}{462} \\ \\ h = 28 \: \: \: \: \underline{\huge\tt{appox}} \\ \\ \rightarrow slant \: height = \sqrt{ {h}^{2} + {r}^{2} } \\ \\ \rightarrow \: \sqrt{ {28}^{2} + {21}^{2} } = \sqrt{1225} = 35$
now, the curved surface area of cone.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \blue{ \huge \tt{\pi rl}}$
$\huge \rightarrow \frac{22}{7} \times 21 \times 35 \\ \\ \huge \rightarrow \frac{22}{ \cancel{7 \: }} \times \cancel{ 21 } ^{ \: \: 3} \times 35 \\ \\ \huge \rightarrow \: 2,310 \: cm^{2}$