Question

The height of a cone is 5 cm. Find the height of another cone, sixteen times its volume and radius equal to two and a half times the radius of the first.

Answer 1

h=5cm
r=2cm

volume=1/3*π*r*r*h
1/3× 22/7×2*2*5
volume is 16 times
16×1/3×22/7×2×2×5

radius is half=1/2*2=1cm

vol= 1/3πr*r*h
16×1/3×22/7×2×2×5=1/3×22/7×1×1×h
height=320cm

Answer 2

The height of the other cone will be 12.8cm

Step-by-step explanation:

Given:

Height of first cone (H)= 5cm

Volume of second cone= 16 times volume of the first cone

Radius of the second cone (r)= 2 and 1/2 times of radius of the first cone

To find:

height of the second cone(h)

Solution:

Let's name the volume of the first cone (V) and the volume of the second cone as (v)

Similarly, the height of the first cone as (H) and of the second cone as (h)

the radius of the first cone as (R) and of the second cone as (r)

According to the given,

radius of the second cone(r)=  $2 \frac{1}{2} R$

Volume of the second cone(v)= 16* volume of the first cone (V)

As we know, Volume of a cone= $\frac{1}{3} \pi r^{2} h$

∴ (⅓)πr²h = 16 × (⅓)πR²H

But, r=  $2 \frac{1}{2} R$

∴ $(2 \frac{1}{2} R)^{2}$ x h= 16 x R²x 5..........(H given as 5cm, $\frac{1}{3} \& \pi$ being eliminated)

∴ $(\frac{5}{2} R)^{2}$x h = 80 x R²...........(solving the mixed fraction $2\frac{1}{2}$ )

∴ $\frac{25}{4} R^{2}$x h = 80R²

∴ h= $\frac{80 X 4}{25}$.........(R² being eliminated)

∴ h= 12.8 cm

Thus, the height of the other cone will be 12.8 cm.