Question

Gobs of Globes is a specialty store which carries a variety of globe-related products. One of their popular products is a globe piggy bank. The standard one they carry has a volume of cubic inches A customer has asked for a custom-made version with a radius triple the size of the standard one. Based on this information, what will be the radius of the custom-made version? A. 15 inches B. 28 inches C. 5 inches D. 11 inches

Answer 1

To find the radius of the custom-made version of the globe piggy bank, we can use the formula for the volume of a sphere and set up an equation. By comparing the volume of the custom-made version to the volume of the standard one, we can determine that the radius of the custom-made version is three times the radius of the standard one. Therefore, the correct answer is A. 15 inches.

Step-by-step explanation:

To find the radius of the custom-made version, we need to understand the relationship between the volume and the radius of a sphere. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius. Since the standard globe piggy bank has a volume of A cubic inches, we can set up the equation A = (4/3)πr^3.

Comparing this equation with the original equation A = (4/3)πr^3, we can see that the volume of the custom-made version is 27 times larger than the standard one. So, the radius of the custom-made version is ∛27 times larger than the radius of the standard one. Since ∛27 = 3, the radius of the custom-made version is 3 times the radius of the standard one. Therefore, the radius of the custom-made version is 3r.

Given that the radius of the standard globe piggy bank is r, the radius of the custom-made version will be 3r. Therefore, the correct answer is A. 15 inches.