Question

the radius and height of the cone are in the ratio 2:3 . if tje volume of a cone is 1617 cubic cm . find the height of a cone.

Answer 1

According to the question, $\frac{r}{h}$  = $\frac{2}{3}$ so we can say that the radius and height of the cone is 2x and 3x,

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

= $\frac{1}{3}$π$(2x)^{2} (3x) = 4π[tex] x^{3}$

= $\frac{88}{7}$$x^{3}$

1617 = $\frac{88}{7}$$x^{3}$

Now you have to solve x and then put h = 3x.

Answer 2

1617=1/3×22/7×(2x)^2×3x. 1617=22/21×4x^2×3x. 1617=22/21×12x^3. 12x^3=1617×21/22. 12x^3=1543.5. x^3= 128.625