Question

A bottle filled with scented oil is made of a half-cylinder-shaped base with a cylindrical pouring spout. Approximately how much space is available to fill the container with oil?

a) 641 cu in
b) 68.5π cu in
c) 807 cu in
d) 90.5π cu in

Answer 1

To find the space available to fill the container with oil, calculate the volumes of the half-cylinder-shaped base and the cylindrical pouring spout separately and then add them together. The correct answer is d) 90.5π cu in.

Step-by-step explanation:

To find the space available to fill the container with oil, we need to calculate the volume of the half-cylinder-shaped base and the cylindrical pouring spout separately and then add them together.

For the half-cylinder-shaped base, we use the formula V = (1/2)πr^2h, where r is the radius of the base and h is the height. Since the base is a half-cylinder, the height is half of the total height of the cylinder.

For the cylindrical pouring spout, we use the formula V = πr^2h, where r is the radius of the spout and h is the height.

After calculating the volumes of the two parts, we add them together to find the total space available to fill the container with oil.

Based on the given information, the correct option is d) 90.5π cu in.