Question

a) the total surface area of a right circular cone of slant height 17cm is 200rt cm per square
1) calculate its radius​

Answer 1

Given :

• Let r be the radius, h be the height and I be the slant height of the given cone, then = 17 cm

To find :

• calculate its radius

Solution :

Total surface area = πr (l + r)

= πr (17 + r) ..................... ( ∴ l = 17 cm)

According to the given data,

πr (17 + r) = 200π

= 17r + r² = 200

= r² +17r - 200

= r² + 25r - 8r - 200 = 0

= r( r + 25) - 8 (r + 25) = 0

= r - 8 or r + 25

= r = 8 or r = -25

but r cannot be negative.

∴ The radius of the cone = 8 cm.

Extra information :

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

Answer 2

Question :

TSA of a right circular cone is 200π cm² and slant height is 17 cm . Find radius

Solution :

Slant height , l = 17 cm

TSA of right circular cone =  200π cm²

TSA of right circular cone = πrl + πr²

:⇒ TSA = πr ( r + l )

$:\implies \sf 200 \cancel{\pi}=\cancel{\pi} r(r+17)$

$:\implies \sf 200=r^2+17r$

$:\implies \sf r^2+17r-200=0$

$:\implies \sf r^2-8r+25r-200=0$

$:\implies \sf r(r-8)+25(r-8)=0$

$:\implies \sf (r-8)(r+25)=0$

$:\implies \sf r=8\ cm\ \; \&\ r \neq-25$

Since radius (lengths) can't be negative .

So , Radius = 8 cm