Question

A gold sphere with a diameter of 120 mm is melted and then cast into a right rectangular prism with a base that is 95 mm long and 85 mm wide. To the nearest millimeter, what is the height of the right rectangular prism?

a) 83 mm
b) 76 mm
c) 78 mm
d) 71 mm

Answer 1

To calculate the height of the right rectangular prism, compute the volume of the gold sphere and set it equal to the volume of the prism. Then, using the given base measurements, solve for the prism's height.

Step-by-step explanation:

To find the height of the right rectangular prism that the gold sphere is cast into, first we need to calculate the volume of the sphere using the formula V = 4/3 π r^3, where r is the radius of the sphere. The sphere has a diameter of 120 mm, so its radius is 60 mm. Substituting into the formula gives us the volume of the sphere, which must be equal to the volume of the prism since melting and recasting does not change the volume of the gold.

The volume of the prism can be found using the formula V = lwh, where l is the length, w is the width, and h is the height of the prism. We know the length is 95 mm and the width is 85 mm, so we can solve for height by rearranging the formula: h = V / (lw).

After substituting the calculated volume of the sphere into the formula for the volume of the prism and solving for height, we find that the height of the prism is 76 mm,