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

3
3

27
27

9
9

30

1 answer

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

The volume \( V \) of a cube is given by the formula:

\[ V = \text{side length}^3 \]

Step 1: Calculate the volume of the freshwater tank.

  • Side length of the freshwater tank = 15 cm \[ V_{\text{freshwater}} = 15^3 = 15 \times 15 \times 15 = 3375 \text{ cm}^3 \]

Step 2: Calculate the volume of the saltwater tank.

  • Side length of the saltwater tank = 45 cm \[ V_{\text{saltwater}} = 45^3 = 45 \times 45 \times 45 = 91125 \text{ cm}^3 \]

Step 3: Find the ratio of the volumes. To determine how many times larger the saltwater tank's volume is, we divide the volume of the saltwater tank by the volume of the freshwater tank:

\[ \text{Ratio} = \frac{V_{\text{saltwater}}}{V_{\text{freshwater}}} = \frac{91125}{3375} \]

Calculating this gives:

\[ \text{Ratio} = 27 \]

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

The answer is: 27