Question

Approximately how many times as great is the volume of a grapefruit with a diameter 16 cm as the volume of a lime with a diameter 8 cm

Answer 1

Answer: The volume of the grapefruit is approximately 8 times as great as the volume of the lime.

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere. This is:

$V=\frac{4}{3}\pi r^3$

Where "r" is the radius.

Volume of the grapefruit

You know that its diameter is 16 centimeters.

Since the radius is half the diameter, you get that its volume is:

$V_g=\frac{4}{3}\pi (\frac{16\ cm}{2}) ^3\\\\V_g= 2,144.66\ cm^3$

Volume of the lime

According to the information given in the exercise, the diameter of the lime is 8 centimeters.

As it was explained above, the radius is half the diameter. Knowing that, you get that volume of the lime is the shown below:

$V_l=\frac{4}{3}\pi (\frac{8\ cm}{2}) ^3\\\\V_l= 268.08\ cm^3$

In order to find approximately how many times as great is the volume of theat grapefruit as the volume of that lime, you need to divide the volumes calculated above. Then:

$\frac{2,144.66\ cm^3}{268.08\ cm^3}\approx8\ times$