Question

Two cylindrical science beakers are similar. The smaller beaker has a radius of 2 centimeters and a height of 4 centimeters. Its volume is about 50 cm³. The larger beaker has a height of about 16 centimeters and a radius of 8 centimeters.

A. The volume of the larger beaker is about 200 cm³.
B. The ratio of the heights of the two beakers is 1:4.
C. The ratio of the volumes of the two beakers is 1:4.
D. The volume of the larger beaker is about 800 cm³.

Answer 1

The volume of the smaller beaker is calculated to be 50.272 cm³ and the volume of the larger beaker is calculated to be 3216.256 cm³, resulting in a ratio of 1:64, not 1:4 as stated in option C.

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder. Given that the smaller beaker has a radius of 2 cm and a height of 4 cm, we can calculate its volume as follows:

V = 3.142 × (2 cm)² × 4 cm = 50.272 cm³

To determine the ratio of the volumes of the two beakers, we need to compare the volumes of the larger beaker and the smaller beaker. The larger beaker has a radius of 8 cm and a height of 16 cm. Using the same formula, we can calculate its volume as follows:

V = 3.142 × (8 cm)² × 16 cm = 3216.256 cm³

Therefore, the ratio of the volumes of the two beakers is 1:64, not 1:4 as stated in option C.