Question

The radius and height of a cone are in the ratio 8:15 and it's volume is 8038.4cm3 .find the radius and the curved surface area of the cone .(take π =3.14 ​

Answer 1

full answer is given in attachment, please refer to it

Answer 2

Answer:

Radius = 16 cm
Area = 1708.16 cm²

(Frank page 271, Exercise 17B, 5th sum, Chp: Area and Volume of Solids)

Step-by-step explanation:

Given

Radius : Height = 8 : 15

Volume = 8038.4 cm³

Let the common multiple be x

∴ Radius = 8x and Height = 15x

Volume = $\pi$ r² h ( $\pi$ = 3.14)

∴ 8038.4 = $\frac{1}{3}$ × 3.14 × 8x × 8x × 15x

$\frac{8038.4}{3.14} = \frac{1}{3}$ × 960x³

2560 = 320x³

8 = x³

2 = x

∴ Radius = 16 cm ( 8 × 2 ) and Height = 30 cm ( 15 × 2 )

Slant height (L) = $\sqrt[2]{h^{2} + r^{2} }$

L = $\sqrt{30^{2} + 16^{2} }$

L = $\sqrt{900 + 256}$

L = $\sqrt{1156}$

L = 34 cm

Curved Surface area = $\pi$ r l

= 3.14 × 16 × 34

= 1708.16 cm²

Hope this helps :))