Question

The radius of a cone is 7 cm and area of curved surface is 176 cm^2 . Find the slant height.

Answer 1

Radius of cone(r) = 7 cm

Curved surface area(C.S.A)= 176cm²

We know, C.S.A. = πrl

⇒ πrl = 176

⇒ 22/7 x 7 x l = 176

or l = 8

Therefore, slant height of the cone is

${ \orange{ \bf{8cm}}}$

${\fcolorbox{blue}{black}{\orange{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: DecentMortal\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$

Answer 2

${ \underline{\sf{\large{\color{pink}{Given}}}}}$

• Radius = 7 cm
• Curved surface area = 176 cm²

${\underline{\sf{\large{\color{pink}{To \: find}}}}}$

• Slant height( l) =?

${\underline{\sf{\large{\color{pink}{Solution}}}}}$

✏️The curved surface area of the cone is defined as the area of the cone excluding the base.

✏️Curved surface Area of the cone is given as :-

${ \underline{ \boxed{ \sf{ \color{grey}{C.S.A = \pi \times r \times l}}}}}$

where

• r denotes the Radius of the cone.

Subsitute the value in the above formula to Find the slant height of the cone.-:

$\sf{ : \implies \: \pi \: rl =176 } \\ \\ \sf{ : \implies \frac{22}{7} \times 7 \times l = 176} \\ \\ \sf{ : \implies \: l = \frac{176}{22} } \\ \\ \sf{:\implies \:l = 8cm }$

$\sf \underline{\therefore\: the\: slant \: height \: is \: 8 \: cm}$

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More To Know !!

✏️Slant height of the cone, L = √(h2+r2)

✏️T.S.A of cone = πr (r + L)

✏️C.S.A of cuboid = 2h(l + b)

✏️ T.S.A of cuboid = 2(lb + bh + lh)

✏️solid sphere T.S.A/C.S.A = 4πr2

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