Question

The radius and height of a solid right circular cone are in the ratio of 5 ratio 12 if its volume is 314 cm cube find its total surface area

Answer 1

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this is the correct answer of the question

Answer 2

Its total surface area is 282.6 sq.cm.

Step-by-step explanation:

The radius and height of a solid right circular cone are in the ratio of 5:12

Let the ratio be x

Radius of cone = 5x

Height of cone = 12 x

Volume of cone = $\frac{1}{3} \pi r^2h =\frac{1}{3} \times 3.14 \times (5x)^2 \times 12x$

We are given that the volume of cone is 314 cubic cm

$314 =\frac{1}{3} \times 3.14 \times (5x)^2 \times (12x)$

$314 = 314x^3$

x = 1

So Height = 5x=5 cm

Radius = 12x=12 cm

Total surface area of cone = $\pi r \sqrt{h^2+r^2}+\pi r^2=3.14 \times 5 \sqrt{12^2+5^2}+3.14 \times 5^2=282.6 cm^2$

Hence its total surface area is 282.6 sq.cm.

#Learn more :

The radius and height of a solid right circular cone are in the ratio of 5:12. If its volume is 314 cm^3. Find total surface areas.

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