Use the image to answer the question.

Question

An illustration shows a rectangular pyramid with a length of 30 centimeters and a perpendicular height of 65 centimeters. The width measurement is shown as a question mark. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.

A rectangular pyramid has a volume of 22,750 cm3
. One of the dimensions of the base is 30 cm, and the altitude is 65 cm. What is the other dimension of the pyramid’s base? Round the answer to the nearest hundredth if necessary.

(1 point)
Responses

35 cm
35 cm

105 cm
105 cm

11.67 cm
11.67 cm

25.27 cm

Answer 1

To find the other dimension of the pyramid's base, we can use the formula for the volume of a rectangular pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Where the Base Area \(A\) of a rectangle is given by:

\[ A = \text{length} \times \text{width} \]

In this case, we know:

• Volume \(V = 22,750 , \text{cm}^3\)
• Length = 30 cm
• Height = 65 cm

Let's denote the width as \(w\). Then the Base Area can be expressed as:

\[ A = 30 \times w \]

Substituting the Volume formula gives us:

\[ 22,750 = \frac{1}{3} \times (30 \times w) \times 65 \]

Now, simplify this equation step by step:

1. Multiply both sides by 3 to eliminate the fraction:

\[ 22,750 \times 3 = 30 \times w \times 65 \]

\[ 68,250 = 30 \times w \times 65 \]

2. Calculate \(30 \times 65\):

\[ 30 \times 65 = 1950 \]

3. Now, substitute \(1950\) back into the equation:

\[ 68,250 = 1950 \times w \]

4. Solve for \(w\):

\[ w = \frac{68,250}{1950} \]

5. Calculating the division:

\[ w = 35 \]

Therefore, the other dimension of the pyramid’s base is 35 cm.

So the correct answer is:

35 cm