Question

1. How many times larger is the volume of a cylinder if the radius is multiplied by 5?
2. How many times smaller is the surface area of a sphere if the radius is multiplied by 1/3?
3. How many times larger is the volume of a cylinder if the radius is multiplied by 3?

Answer 1

(1) The volume of a cylinder will be 25 times larger if the radius is multiplied by 5.

(2) The surface area of a sphere will be $(\frac{1}{9})$ times smaller if the radius is multiplied by (1/3).

(3) The volume of a cylinder will be 9 times larger if the radius is multiplied by 3.

Step-by-step explanation:

(1) We have to find how many times larger is the volume of a cylinder if the radius is multiplied by 5.

Firstly, as we know that the volume of a cylinder is given by the formula;

Volume of a cylinder = $\pi r^{2}h$

where, r = radius of a cylinder and h = height of the cylinder.

Now, if the radius is multiplied by 5, then the new volume of a cylinder will be;

    Volume of a cylinder = $\pi (5r)^{2}h$

                                        = $25\times ( \pi r^{2}h)$

This means that the volume of a cylinder will be 25 times larger if the radius is multiplied by 5.

(2) We have to find how many times smaller is the surface area of a sphere if the radius is multiplied by 1/3.

Firstly, as we know that the surface area of a sphere is given by the formula;

Surface area of a sphere = $4\pi r^{2}$     where; r = radius of a cylinder

Now, if the radius is multiplied by (1/3), then the new surface area of a sphere will be;

    Surface area of a sphere = $4\pi (\frac{1}{3}\times r)^{2}$

                                               = $\frac{1}{9}\times ( 4\pi r^{2})$

This means that the surface area of a sphere will be $(\frac{1}{9})$ times smaller if the radius is multiplied by (1/3).

(3) We have to find how many times larger is the volume of a cylinder if the radius is multiplied by 3.

Firstly, as we know that the volume of a cylinder is given by the formula;

Volume of a cylinder = $\pi r^{2}h$

where, r = radius of a cylinder and h = height of the cylinder.

Now, if the radius is multiplied by 3, then the new volume of a cylinder will be;

    Volume of a cylinder = $\pi (3r)^{2}h$

                                        = $9\times ( \pi r^{2}h)$

This means that the volume of a cylinder will be 9 times larger if the radius is multiplied by 3.