Question

Find the csa of a right circular cone of height 15 cm and base diameter is 16 cm

Answer 1

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

$\green{\tt{\therefore{C.S.A\:of\:cone=427.04\:cm^{2}}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Height \: of \: cone = 15 \: cm \\ \\ \tt: \implies Diameter \: of \: cone = 16 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies C.S.A\: of \:cone = ?$

• According to given question :

$\tt{ \circ \: Height(h) = 16 \: cm} \\ \\ \tt \circ \: radius(r) = 8 \: cm \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ \tt: \implies {l}^{2} = {h }^{2} + {r}^{2} \\ \\ \tt: \implies {l}^{2} = {15}^{2} + {8}^{2} \\ \\ \tt: \implies {l}^{2} = 225 + 64 \\ \\ \tt: \implies {l}^{2} = 289 \\ \\ \tt: \implies l = \sqrt{289} \\ \\ \tt: \implies l = 17 \: cm \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies C.S.A\: of \: cone = \pi rl \\ \\ \tt: \implies C.S.A\: of \: cone = 3.14 \times 8 \times 17 \\ \\ \green{\tt: \implies C.S.A\: of \: cone = 427.04\: {cm}^{2} }$

Answer 2

$\bf{given}$

• height, h=15cm
• diameter, d=16cm
• r=d/2=>16/2=>8cm

$\bf \red{formula \: used}$

$\bf \purple{CSA \: of \: a \: cone = πrl}$

$\bf \orange{solution}$

By pythagoras therome

$l = \sqrt{r {}^{2} + h {}^{2} }$

$\blue{l = \sqrt{8 {}^{2} + 15 {}^{2} } }$

$\pink{l = \sqrt{64 + 225} }$

$\green{l = \sqrt{284} }$

$\red{l = 17}$

Now ,

$\orange{CSA \: of \: a \: cone = πrl}$

$= \frac{22}{7} \times 8 \times 17$

$=\frac{22}{7} \times 136$

$\purple{427.42}$