Question

if the radius of a cone is increased by 100% its volume is increased by​

Answer 1

We know that the volume of any cone having the radius r is =

⅓ × πr²h

Suppose the height = 1 in each case.

So let the original radius = 1

So the volume = ⅓ × π×1×1 = ⅓π unit³

Then , according to the question , new radius = 100×1 = 100

Then , new volume = ⅓πr²h = ⅓ × π × (100)²×1 = ⅓ × 10000 = ⅓π10000

The new volume is increased by 10000 times.

Answer 2

Answer:

Step-by-step explanation:

V(cone) = (1/3)×pi×(r^2)×h, where h is the height and r is the radius of the base.

if the radius is increased 100%, then r becomes 2r, then the volume becomes

V(cone) = (1/3)×pi×( (2r)^2 )×h

=(1/3)×pi×(4(r^2))×h

= 4×(1/3)×pi×(r^2)×h.

the volume is increased by 400%.