Question

The radius of the large sphere is double the radius of the

small sphere
How many times is the volume of the large sphere than the
small sphere?a.2 b.4 c.6 d.8

Answer 1

Answer: Option d

`(V_2)/(V_1)=8`

Explanation:

The volume of a sphere is calculated using the following formula

`V=(4)/(3)\pi r^3`

Where r is the radius of the sphere and V is the volume.

If the radius of the small sphere is r and the volume is
`V_1` then:

`V_1=(4)/(3)\pi r^3`

Let's call
`V_2` the volume of the large sphere. We know that it has a radius of 2r. So:

`V_2=(4)/(3)\pi (2r)^3`

`V_2=(4)/(3)*8\pi r^3`

Now we calculate the quotient of the volumes

`(V_2)/(V_1)=((4)/(3)*8\pi r^3)/((4)/(3)\pi r^3)\\\\(V_2)/(V_1)=(8r^3)/(r^3)\\\\(V_2)/(V_1)=8`

The answer is the option d

Answer 2

d. 8

Explanation:

The volume of a sphere = 4/3πr³

Let the radius of the smaller sphere be r, then the volume of the large sphere will be 2 r

Finding the volumes of the 2 gives:

volume of large sphere = 4/3π (2r)³

= 32/3πr³

Volume of the smaller sphere = 4/3πr³

Dividing the two volumes we get the ratio of their volumes

32/3πr³÷4/3πr³= 8