Question

The total surface area of a cone is 704 sq.m and radius of it's base is 7cm find the slant height of the cone

Answer 1

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

$\green{\tt{\therefore{Slant\:height=3199.93\:m}}}$

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

$\green{\underline \bold{Given :}} \\ \tt:\implies T.S.A\: of \: cone = 704 \: {m}^{2} \\ \\ \tt:\implies Radius \: of \: cone = 7 \: cm \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Slant \: height =?$

• According to given question :

$\tt \circ \: Radius = \frac{7}{100} = 0.07 \: m \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies T.S.A \: of \:cone = \pi r(l + r) \\ \\ \tt: \implies 704 = \frac{22}{7} \times 0.07(l + 0.07) \\ \\ \tt: \implies \frac{704 \times 7}{22 \times 0.07} = l + 0.07 \\ \\ \tt: \implies 32 \times 100 = l + 0.07 \\ \\ \tt: \implies 3200 - 0.07 = l \\ \\ \green{\tt: \implies l = 3199.93 \: m } \\ \\ \green{\tt \therefore Slant \: height \:is \: 3199.93 \: m}$

Answer 2

Step-by-step explanation:

$\large{\underline{\underline{\sf Given:-}}}$

• $\sf TSA_{cone}=704 \: m^2$
• $\sf Radius_{base}=7 \:cm =0.07\: m$

$\large{\underline{\underline{\sf To \: find:-}}}$

• $\sf Slant \: height_{cone}=?$

$\large{\underline{\underline{\sf Solution:-}}}$

$\sf \bf We \: know \: that,$

$\underline{\boxed{\sf TSA_{cone} = πr(r+l)}}$

$\sf πr(r+l) = 704$

$\sf \dfrac{22}{7}×0.07(0.07+l)=704$

$\sf 22×0.01(0.07+l)=704$

$\sf 0.07+l=\dfrac{704}{22×0.01}$

$\sf 0.07+l=3200$

$\sf l=3200-0.07$

$\sf l=3199.93 \: m$