A tent in the shape of a triangular prism is set up at a camping site. Use the measurements to calculate the volume of the tent. Report the answer using the correct number of significant figures. Remember, the volume formula for a triangular prism is given by upper V equals upper B h.

A three-dimensional shape has three rectangular sides with triangular bases on either end. On one of the triangular faces, the vertical height is labeled 4 centimeters and the width is labeled 6 centimeters. The length of one of the rectangular sides is labeled 11 centimeters.
(1 point)
Responses

132 centimeters squared
Image with alt text: 132 centimeters squared

130 centimeters squared
Image with alt text: 130 centimeters squared

100 centimeters squared
Image with alt text: 100 centimeters squared

140 centimeters squared
Image with alt text: 140 centimeters squared

1 answer

To calculate the volume of the triangular prism (the tent), we can use the formula \( V = B \times h \), where \( B \) is the area of the triangular base and \( h \) is the height (or length) of the prism.

  1. Calculate the area of the triangular base (B): The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the width (base) is 6 cm and the height is 4 cm: \[ A = \frac{1}{2} \times 6 , \text{cm} \times 4 , \text{cm} = \frac{1}{2} \times 24 , \text{cm}^2 = 12 , \text{cm}^2 \]

  2. Now calculate the volume (V) using the height (length) of the prism: The height of the prism is given as 11 cm: \[ V = B \times h = 12 , \text{cm}^2 \times 11 , \text{cm} = 132 , \text{cm}^3 \]

  3. Significant figures: Both the base (6 cm) and height (4 cm) have 1 significant figure after the leading number, and the length (11 cm) has 2 significant figures. Therefore, the final volume should be reported with the least number of significant figures, which is 1.

The correctly reported volume of the tent is 130 cm³ (rounded to 2 significant figures, which has been simplified from 132).

So, the correct answer is:

130 centimeters cubed.