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Math  /  Geometry

Question0 1 point A fruit crate has square ends and is twice as long as it is wide. Find the volume of the crate (in cubic inches) if its width is 20 in.

Studdy Solution

STEP 1

1. The crate has square ends, implying that the width and height of the crate are equal.
2. The crate is twice as long as it is wide.
3. The width of the crate is given as 20 inches.

STEP 2

1. Define the dimensions of the crate based on the given width.
2. Calculate the length of the crate using the given relationship between length and width.
3. Use the dimensions to calculate the volume of the crate using the volume formula for a rectangular prism.

STEP 3

Let the width of the crate be denoted by w w . Given that w=20 w = 20 inches.

STEP 4

Since the ends of the crate are square, the height h h of the crate is also 20 20 inches.

STEP 5

Given that the crate is twice as long as it is wide, the length l l of the crate is 2×w 2 \times w .
l=2×20=40 inches l = 2 \times 20 = 40 \text{ inches}

STEP 6

The volume V V of a rectangular prism is given by the formula:
V=l×w×h V = l \times w \times h
Substituting the given dimensions, we get:
V=40×20×20 V = 40 \times 20 \times 20

STEP 7

Calculate the volume:
V=40×20×20=16000 cubic inches V = 40 \times 20 \times 20 = 16000 \text{ cubic inches}
Solution: The volume of the crate is 16000 16000 cubic inches.

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