Question

the height and radius of base of cone each is increased by 100 %.how much is the volume of the cone then increased by

Answer 1

Answer:

Step-by-step explanation:

Saying something “increased by 100%” is same as saying it “became 2 times” of what it was.

So, if for a cone, radius and height are increased by 100%, then we can say that if original radius was R and height was H, then:

new radius = 2R and new height = 2H.

Now, volume (V) of a cone is given by the formula:

V = 1/3* π*(radius)^2 * (height)

So, in 1st case,

V1 = 1/3* π* (R)^2 * (H)

while in 2nd case

V2 = 1/3* π* (2R)^2 * (2H)  

Hence, V2 = 8*[1/3* π* (R)^2 * (H)]

Hence, V2 = 8*(V1)

Thus, when radius and height of a cone are increased by 100%, volume becomes 8 times which is same as saying volume increases by 700%