Question

if the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic meter. find its perpendicular height an slant height (pai = 3.14)

Answer 1

see this will be answer I think...

Answer 2

Perpendicular height is 12 meter

Slant height is 13 m.

Solution:

The ratio of radius to height of the cone = 5 : 12

Volume of the cone = 314 cubic meter

Let the radius of base and the perpendicular height be 5x and 12x respectively.

Volume of the cone = $\frac{1}{3}\pi r^2 h$

$\Rightarrow\frac{1}{3}\pi r^2 h=314$

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

$\Rightarrow \frac{1}{3} \times 3.14 \times 300 x^{3}=314$

$\Rightarrow 314 x^{3}=314$

Divide by 314 on both sides of the equation, we get

$\Rightarrow x^{3}=1$

Taking cube root on both sides of the equation, we get

$\Rightarrow x=1$

Perpendicular height of the cone = 12 × 1 = 12 meter

Radius of the cone = 5 × 1 = 5 meter

To find the slant height of the cone:

Let l be the slant height of the cone.

$\text{(Slant height)} ^{2}= (Perpendicular height) ^{2}+ (Radius) ^{2}$

$\Rightarrow{ l}^{2}=(12)^{2}+(5)^{2}$

$\Rightarrow l^{2}=144+25$

$\Rightarrow l^{2}=169$

Taking square root on both sides of the equation, we get

$\Rightarrow l=13$

slant height = 13 m

Hence the perpendicular height is 12 meter and the slant height is 13 m

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