Let's solve each question step by step.
Question 1
To find the volume of a rectangular prism, we use the formula: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given:
- Length = 15 yards
- Width = 8 yards
- Height = 5 yards
Calculating the volume: \[ \text{Volume} = 15 \times 8 \times 5 = 600 \text{ cubic yards} \]
Answer: 600 cubic yards
Question 2
First, we convert the mixed numbers to improper fractions.
- Convert dimensions:
- \( 2 \frac{3}{4} = \frac{11}{4} \) inches
- \( 16 \frac{1}{2} = \frac{33}{2} \) inches
Now, calculate the volume: \[ \text{Volume} = \frac{11}{4} \times \frac{33}{2} \times 4 \]
Simplifying: \[ \text{Volume} = \frac{11 \times 33}{4 \times 2} \times 4 = \frac{11 \times 33}{2} = \frac{363}{2} = 181.5 \text{ in}^3 \]
Answer: One hundred eighty-one and one-half in³ (181.5 in³)
Question 3
We can find the area of the base \( B \) using the formula: \[ \text{Volume} = B \times \text{Height} \]
Given:
- Volume = 26,214 m³
- Height = 17 m
Rearranging: \[ B = \frac{\text{Volume}}{\text{Height}} = \frac{26,214}{17} = 1,542 \text{ m}^2 \]
Answer: 1,542 m²
Question 4
Calculating the volume using the formula: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given:
- Length = 18 inches
- Width = 13 inches
- Height = 6 inches
Calculating: \[ \text{Volume} = 18 \times 13 \times 6 = 1,404 \text{ in}^3 \]
Answer: 1,404 in³
Question 5
To find the volume: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given:
- Length = 32 inches
- Width = 50 inches
- Height = 48 inches
Calculating: \[ \text{Volume} = 32 \times 50 \times 48 = 76,800 \text{ in}^3 \]
Answer: 76,800 in³
Question 6
We can use the formula for volume rearranged to find height: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given:
- Volume = 240 ft³
- Length = 8 feet
- Width = 6 feet
Rearranging for height: \[ \text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Width}} \] \[ \text{Height} = \frac{240}{8 \times 6} = \frac{240}{48} = 5 \text{ feet} \]
Answer: 5 feet
Question 7
Using the formula for volume again: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given:
- Volume = 6,142.5 cm³
- Height = 16.25 cm
- Length = 28 cm
Rearranging for width: \[ \text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}} \] \[ \text{Width} = \frac{6,142.5}{28 \times 16.25} \]
Calculating: \[ 28 \times 16.25 = 455 \] \[ \text{Width} = \frac{6,142.5}{455} = 13.5 \text{ cm} \]
Answer: 13.5 cm