Question

Anna Beth has a freshwater fish tank and a saltwater fish tank. They are both cubes. The side length of the freshwater tank is 15 cm. The side length of the saltwater tank is 45 cm. How many times larger is the volume of the saltwater tank than the volume of the freshwater tank? (1 point) Responses 9 9 27 27 3 3 30

Answer 1

To find how many times larger the volume of the saltwater tank is compared to the volume of the freshwater tank, we first need to calculate the volumes of both tanks.

The volume $V$ of a cube is given by the formula:

$$V={\text{side length}}^3$$

1. Calculate the volume of the freshwater tank (side length = 15 cm):

$$V_{\text{freshwater}}={15}^3=15\times 15\times 15=3375{\text{ cm}}^3$$

2. Calculate the volume of the saltwater tank (side length = 45 cm):

$$V_{\text{saltwater}}={45}^3=45\times 45\times 45=91125{\text{ cm}}^3$$

3. Now, find how many times larger the saltwater tank is than the freshwater tank:

$$\text{Factor}=\frac{V_{\text{saltwater}}}{V_{\text{freshwater}}}=\frac{91125}{3375}$$

Calculating this gives:

$$\text{Factor}=\frac{91125÷3375}{3375÷3375}=\frac{27}{1}=27$$

Thus, the volume of the saltwater tank is 27 times larger than the volume of the freshwater tank.

The answer is 27.