Question

Find the slant height of the cone whose radius is 7cm and total surface area is 704 square cm

Answer 1

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

$\green{\tt{\therefore{Slant\:height=25\:cm}}}$

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

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

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies T.S.A \: of \: cone = 704 \\ \\ \tt: \implies \pi r(l + r)= 704 \\ \\ \tt: \implies l + r = \frac{704}{\pi r} \\ \\ \tt: \implies l+ 7 = \frac{704 \times 7}{22 \times 7} \\ \\ \tt: \implies l+ 7 = 32\\ \\ \tt: \implies l= 32 - 7 \\ \\ \green{\tt: \implies l= 25\: cm}\\\\ \green{\tt\therefore Slant\:height\:of\:cone\:is\:25\:cm}$

Answer 2

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$\tt{\huge{\purple{ ................. }}}$

QUESTION :

Find the slant height of the cone whose radius is 7cm and total surface area is 704 square cm.

SOLUTION :

From the above Question, we can gather the following information....

The radii if the cone is 7 cm.

The total surface area of the cone is 704 sq cm.

We know that:

TSA of a cone = 2πrl + 2πr^ 2

=> TSA = 2πr ( l + r )

r = 7 cm

TSA = 44(l + 7 )

But TSA = 704 cm ^ 2

Solving,

L + 7 = 32

=> L = 25 cm.

So the slant height of the cone is 25 cm.

ANSWER :

The slant height of the cone is 25 cm.