Question

2.
15ft
10ft
9ft

4.
21m
11m
13m

5.
17mm
6mm
19mm

7.
18cm

Explanation:

Calculate the volume of the rectangular prism in Question 2

The first figure is a rectangular prism with a length of \(9\text{ ft}\), a width of \(10\text{ ft}\), and a height of \(15\text{ ft}\).
The volume \(V\) of a rectangular prism is calculated using the formula:

$$V = \text{length} \times \text{width} \times \text{height}$$

Substituting the given values:

$$V = 9\text{ ft} \times 10\text{ ft} \times 15\text{ ft} = 1350\text{ ft}^3$$

Calculate the volume of the triangular prism in Question 4

The second figure is a right triangular prism. The base is a right-angled triangle with legs of \(11\text{ m}\) and \(13\text{ m}\). The height (length) of the prism is \(21\text{ m}\).
Using the Triangle Area Formula, the area of the triangular base \(B\) is:

$$B = \frac{1}{2} \times \text{base} \times \text{height of triangle} = \frac{1}{2} \times 11\text{ m} \times 13\text{ m} = 71.5\text{ m}^2$$

The volume \(V\) of the prism is:

$$V = B \times \text{height of prism} = 71.5\text{ m}^2 \times 21\text{ m} = 1501.5\text{ m}^3$$

Calculate the volume of the triangular prism in Question 5

The third figure is a triangular prism. The base is a triangle with a base length of \(19\text{ mm}\) and a corresponding Altitude of a Triangle (height) of \(6\text{ mm}\). The height of the prism is \(17\text{ mm}\).
Using the Triangle Area Formula, the area of the triangular base \(B\) is:

$$B = \frac{1}{2} \times 19\text{ mm} \times 6\text{ mm} = 57\text{ mm}^2$$

The volume \(V\) of the prism is:

$$V = B \times \text{height of prism} = 57\text{ mm}^2 \times 17\text{ mm} = 969\text{ mm}^3$$

Answer:

Question 2

$$V = 1350\text{ ft}^3$$

Question 4

$$V = 1501.5\text{ m}^3$$

Question 5

$$V = 969\text{ mm}^3$$