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. Approximately what is the volume of the larger beaker?

A. 3,200 cm³
B. 1,600 cm³
C. 800 cm³
D. 200 cm³

Answer 1

To find the volume of the larger beaker, we use the principle of similar figures. The volume of the larger beaker is approximately 3,200 cm³.

Step-by-step explanation:

To find the volume of the larger beaker, we can use the principle of similar figures. Since the beakers are similar, the ratio of their heights is the same as the ratio of their volumes. The smaller beaker has a height of 4 cm and a volume of 50 cm³. The larger beaker has a height of 16 cm, so the ratio of their heights is 16/4 = 4.

Since the volumes of similar figures are proportional to the cubes of their corresponding sides, we can find the volume of the larger beaker by multiplying the volume of the smaller beaker by the cube of the ratio of their heights.

Volume of larger beaker = Volume of smaller beaker * (ratio of heights)³ = 50 cm³ * 4³ = 50 cm³ * 64 = 3200 cm³.

Therefore, the volume of the larger beaker is approximately 3,200 cm³, which is option A.