Question

The height of a cone is 5 m find the height of another cone whose volume is 16 times its volume and radius equal to its diameter

Answer 1

Answer:

Height = 20 cm

Step-by-step explanation:

h₁ = 5 cm, h₂ , r₂ = 2r₁

V₁ = πr₁²h₁/3 => 5πr₁²/3 cm³

V₂ = πr₂²h₂/3 =>π(2r₁)²h₂/3 => 4πr₁²h₂/3

Now, V₂ = 16 V₁

=> 4πr₁²h₂/3 = 16(5πr₁²/3 cm³) =>  4πr₁²h₂/3 = 80πr₁²/3 cm³

=> 3(4πr₁²h₂) = 3(80πr₁²) => 12πr₁²h₂ = 240πr₁²

=> h₂ = 240πr₁²/12πr₁²

=> h₂ = 20 cm

Mark it as the brainliest!!

:)

Answer 2

Answer:

20cm

Step-by-step explanation:

Given that, the Volume of Cone 1 is sixteen times the volume of Cone 2 and the radius of Cone 2 is equal to the diameter of Cone 1.

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

So the equation is,

$16*\frac{1}{3}\pi r^{2}h = \frac{1}{3}\pi d^{2}H$

$16*\frac{1}{3}\pi r^{2}*5= \frac{1}{3}\pi (2r)^{2}H$

$16*r^{2}*5 = (2r)^{2}H$     [Cancel $\frac{1}{3} \pi$ on both sides]

$16*r^{2}*5 = (4r^2)H$

$16*5 = 4*H$     [Cancel $r^{2}$ on both sides]

$5*4 = H$

$20 = H$

Therefore, the height of Cone 2 is equal to 20cm.