Frank keeps his pet iguana in a glass tank that is shaped like a rectangular prism. The height of the tank is 11 inches, the width is 34.5 inches, and the length is 25 inches. What is the best estimate for the volume of the tank in cubic feet? Remember 12 inches = 1 foot. A. 4 ft3 B. 6 ft3 C. 9 ft3 D. 12 ft3
The Correct Answer and Explanation is:
To estimate the volume of Frank’s glass tank, we can use the formula for the volume of a rectangular prism:
Volume = length × width × height
Given:
- Height = 11 inches
- Width = 34.5 inches
- Length = 25 inches
Step 1: Calculate the volume in cubic inches. Volume=25 in×34.5 in×11 in=9,487.5 in3\text{Volume} = 25 \, \text{in} \times 34.5 \, \text{in} \times 11 \, \text{in} = 9,487.5 \, \text{in}^3Volume=25in×34.5in×11in=9,487.5in3
Step 2: Convert the volume from cubic inches to cubic feet. Since 12 in=1 ft12 \, \text{in} = 1 \, \text{ft}12in=1ft, we know that there are 123=1,72812^3 = 1,728123=1,728 cubic inches in 1 cubic foot. Volume in cubic feet=9,487.5 in31,728 in3/ft3≈5.5 ft3\text{Volume in cubic feet} = \frac{9,487.5 \, \text{in}^3}{1,728 \, \text{in}^3/\text{ft}^3} \approx 5.5 \, \text{ft}^3Volume in cubic feet=1,728in3/ft39,487.5in3≈5.5ft3
Step 3: Estimate the volume. Since 5.5 cubic feet is closest to 6 cubic feet, the best estimate for the volume of the tank is:
Answer: B. 6 ft³
Explanation:
The question asks for the best estimate for the volume, so we rounded our calculation of 5.5 cubic feet to the nearest option provided. While more precise calculations would give us an exact answer, it’s typical to round to the closest available choice when estimating. In this case, 6 cubic feet is the closest estimate to the actual volume.
