rectangular prism: height 7 feet, width 4 feet and length 3 feet

Find the volume

Cylinder: radius 3.5 feet and height 7 feet

Find the volume

Van cargo space measures 8 feet tall by 5 feet wide by 13 feet deep.

find the volume

instruments will take up about 37 cubic feet

Based on the volume measurements, will the objects fit in the van? prove your answer

Prism V = h * w * l

V = 7 * 4 * 3 = ?

Cylinder V = π r^2 h

Van V = (8 * 5 * 13) -37 = ?

You can do the calculations.

this is wrong

84 ft for rectangular prism

To find the volume of a rectangular prism, you need to multiply its length, width, and height. Let's calculate the volumes of the given objects one by one.

1. Rectangular Prism:
Volume = Length x Width x Height
Volume = 3 feet x 4 feet x 7 feet
Volume = 84 cubic feet

2. Cylinder:
In a cylinder, the volume can be calculated by multiplying the area of the base (π * radius^2) by the height.
Volume = π * (radius^2) * Height
Volume = 3.14 * (3.5 feet^2) * 7 feet
Volume ≈ 269.43 cubic feet

3. Van Cargo Space:
Volume = Length x Width x Height
Volume = 8 feet x 5 feet x 13 feet
Volume = 520 cubic feet

Now, let's determine if the objects will fit in the van. We already know the volume of the van cargo space is 520 cubic feet. The instruments will take up about 37 cubic feet.

Total volume of the objects (rectangular prism and cylinder) = Volume of Rectangular Prism + Volume of Cylinder
Total volume = 84 cubic feet + 269.43 cubic feet
Total volume ≈ 353.43 cubic feet

Since the total volume of the objects is less than the volume of the van cargo space, i.e., 353.43 cubic feet < 520 cubic feet, the objects will fit in the van.