Question

Anya has two cylindrical coffee mugs. The larger has a height of 15 cm, and the smaller has a height of 10 cm, both with an internal diameter of 8 cm. What is the closest to the difference in cm³ between their volumes?

a) 160 cm³
b) 240 cm³
c) 320 cm³
d) 400 cm³

Answer 1

To find the difference in volume between the two cylinders, calculate the volume of each cylinder and subtract the smaller volume from the larger volume. The closest option to the difference in cm³ between their volumes is 400 cm³.

Step-by-step explanation:

To find the difference in volume between the two cylinders, we need to calculate the volume of each cylinder and subtract the smaller volume from the larger volume. The formula for the volume of a cylinder is V = πr²h.

The larger cylinder has a height of 15 cm, so its volume is V = π(4 cm)²(15 cm) = 240π cm³.

The smaller cylinder has a height of 10 cm, so its volume is V = π(4 cm)²(10 cm) = 160π cm³.

Now we subtract the smaller volume from the larger volume: 240π cm³ - 160π cm³ = 80π cm³.

Since π is approximately 3.14, the closest option to the difference in cm³ between their volumes is 80π cm³ ≈ 251.2 cm³. Therefore, the closest option is d) 400 cm³.