Question

Sophia is setting up two fish tanks for her pet fish. One tank is a rectangular prism, and the other is a cylinder. She needs to determine which tank will hold more water so she can put her larger fish in the tank with more volume.

The rectangular prism tank has a length of 30 cm, a width of 20 cm, and a height of 50 cm.

The cylindrical tank has a radius of 15 cm and a height of 50 cm.



Your task:

1. Calculate the volume of each fish tank.

2. Compare the volumes of the two tanks to figure out which one holds more water.

3. Show all your work, including the formulas you use for calculating the volume of both shapes.

4. Based on your calculations, which tank should hold the bigger fish?

(4 points)

Answer 1

1) Formulas
- Rectangular prism: V = length × width × height
- Cylinder: V = π × radius^2 × height

2) Rectangular prism volume
V_rect = 30 cm × 20 cm × 50 cm
V_rect = (30 × 20) × 50 = 600 × 50 = 30,000 cm³
(= 30,000 cm³ = 30.0 L since 1 L = 1000 cm³)

3) Cylindrical tank volume
V_cyl = π × (15 cm)^2 × 50 cm = π × 225 × 50 = 11,250π cm³
Numerical value: V_cyl ≈ 11,250 × 3.14159 = 35,342.92 cm³
(≈ 35.34 L)

4) Comparison and conclusion
- Rectangular: 30,000 cm³ (30.0 L)
- Cylinder: ≈ 35,342.9 cm³ (≈ 35.34 L)

The cylindrical tank holds more water (about 5,342.9 cm³ or 5.34 L more). Put the bigger fish in the cylindrical tank.