1.) The volume of a rectangular prism is calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
For the given dimensions:
Length \( = 5 \) inches, Width \( = 4 \) inches, Height \( = 3 \) inches.
\[ \text{Volume} = 5 \times 4 \times 3 = 60 \text{ cubic inches} \]
Answer: 60 cubic inches
2.) To determine which box has a volume of at least 48 cubic feet, we calculate the volume of each box using the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
-
Box 1:
Length \( = 4 \) feet, Width \( = 4 \) feet, Height \( = 4 \) feet
\[ \text{Volume} = 4 \times 4 \times 4 = 64 \text{ cubic feet} \] -
Box 2:
Length \( = 11 \) feet, Width \( = 2 \) feet, Height \( = 2 \) feet
\[ \text{Volume} = 11 \times 2 \times 2 = 44 \text{ cubic feet} \] -
Box 3:
Length \( = 8 \) feet, Width \( = 2 \) feet, Height \( = 3 \) feet
\[ \text{Volume} = 8 \times 2 \times 3 = 48 \text{ cubic feet} \]
The box Ted should choose is Box 1, since it has a volume of 64 cubic feet (the highest volume over 48 cubic feet).
Answer: Box 1
3.) The volume of a box can also be calculated using the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
Given: Base area \( = 20 \) square inches, Height \( = 3 \) inches.
\[ \text{Volume} = 20 \times 3 = 60 \text{ cubic inches} \]
Answer: 60 cubic inches
4.) For a rectangular prism, the volume formula is:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given: Volume \( = 60 \) cubic centimeters, Length \( = 3 \) cm, Height \( = 5 \) cm.
Let Width be \( w \):
\[ 60 = 3 \times w \times 5 \]
\[ 60 = 15w \]
\[ w = \frac{60}{15} = 4 \text{ cm} \]
Answer: 4 cm