Question

The ratio of radius to height of a right circular cone is 4:9 if it's volume is 1507 m cube find its slant height and radius Take Pai 3.14

Answer 1

The slant height and radius are 21.214 m and 8.616 m respectively.

Step-by-step explanation:

The ratio of radius to height of a right circular cone is 4:9

Let the ratio be x

So, radius = 4x

Height = 9x

Volume of cone = $\frac{1}{3} \pi r^2 h=\frac{1}{3} \times 3.14 \times (4x)^2(9x)$

We are given that it's volume is 1507 m cube

So,$\frac{1}{3} \times 3.14 \times (4x)^2(9x)=1507$

$\frac{1}{3} \times 3.14 \times 144x^3=1507$

$x^3=\frac{1507 \times 3}{3.14 \times 144}$

$x=\sqrt[3]{\frac{1507 \times 3}{3.14 \times 144}}$

$x=2.154$

Radius = 4x= 4(2.154)= 8.616 m

Height = 9x=9(2.154)=19.386 m

Slant height =$\sqrt{h^2+r^2}=\sqrt{19.386^2+8.616^2}=21.214$

Hence The slant height and radius are 21.214 m and 8.616 m respectively.

#Learn more:

The radius and the height of a right circular cone are in the ratio 5 : 12 and volume is 2512 cm cube find the slant height and the radius of the base of cone? Take Pi 3.14.

https://brainly.in/question/2257899

Answer 2

Step-by-step explanation:

ratio of radius to height of a right circular cone 4:9

let the radius be 4x

height be 9x

volume of cone=1/3πr^2h

=x=2.154

radius =4x=4×2.154=8.616m

height=9x=9×2.154=19.386m

slant height=21.214 m