Question

the radius and the height of a right circular cone and are in ratio of 5: 12 and its volume is 2512 cubic centimetre find the curved surface area and the total surface area of cone use Pi is equal to 3.14

Answer 1

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Answer 2

Curved surface area of cone = 816.4 sq.cm.

Total surface area of cone =1130.4 sq.cm.

Step-by-step explanation:

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

Let the ratio be x

Radius = 5x

Height = 12 x

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

We are given that Its volume is 2512 cubic centimeter

So,  $\frac{1}{3} \times 3.14 \times (5x)^2 (12x) = 2512$

$314x^3=2512$

$x=\sqrt[3]{\frac{2512}{314}}$

x=2

Radius = 5x =5(2)=10 cm

Height = 12 x =12(2)=24 cm

Curved surface area of cone =$\pi r \sqrt{h^2+r^2}=3.14 \times 10 \times \sqrt{24^2+10^2}=816.4 cm^2$

Total surface area of cone =$\pi r \sqrt{h^2+r^2} + \pi r^2=3.14 \times 10 \times \sqrt{24^2+10^2}+3.14 \times 10^2= 1130.4 cm^2$

#Learn more:

The height of a cone is 16cm and its base radius is 12cm . find the curved surface area and the total surface area of the cone use

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