Question

calculate the surface area and volume of the rectangular prism.
calculate the surface area and volume of the cube.
the trailer on a rig has the dimensions 45 ft by 8.5 ft by 28 ft. how much space is available inside the trailer?

Explanation:

Rectangular Prism (12 in, 9 in, 3 in)

Surface Area

Step1: Recall formula for SA of rectangular prism

The formula for the surface area (\(SA\)) of a rectangular prism is \(SA = 2(lw + lh + wh)\), where \(l = 12\) in, \(w = 9\) in, \(h = 3\) in.

Step2: Substitute values into the formula

First, calculate \(lw = 12\times9 = 108\), \(lh = 12\times3 = 36\), \(wh = 9\times3 = 27\). Then, \(lw + lh + wh = 108 + 36 + 27 = 171\). Multiply by 2: \(SA = 2\times171 = 342\) square inches.

Volume

Step1: Recall formula for volume of rectangular prism

The formula for the volume (\(V\)) of a rectangular prism is \(V = lwh\).

Step2: Substitute values into the formula

\(V = 12\times9\times3 = 324\) cubic inches.

Cube (3.2 m side)

Surface Area

Step1: Recall formula for SA of cube

The formula for the surface area (\(SA\)) of a cube is \(SA = 6s^2\), where \(s = 3.2\) m.

Step2: Substitute values into the formula

\(s^2 = 3.2^2 = 10.24\), then \(SA = 6\times10.24 = 61.44\) square meters.

Volume

Step1: Recall formula for volume of cube

The formula for the volume (\(V\)) of a cube is \(V = s^3\).

Step2: Substitute values into the formula

\(V = 3.2^3 = 3.2\times3.2\times3.2 = 32.768\) cubic meters.

Trailer (45 ft, 8.5 ft, 28 ft)

Volume (Space Inside)

Step1: Recall formula for volume of rectangular prism

The space inside the trailer is its volume, and the formula for the volume (\(V\)) of a rectangular prism is \(V = lwh\), where \(l = 45\) ft, \(w = 8.5\) ft, \(h = 28\) ft.

Step2: Substitute values into the formula

\(V = 45\times8.5\times28 = 45\times238 = 10710\) cubic feet.

Answer:

s:

• Rectangular Prism:

Surface Area: \(342\) in²
Volume: \(324\) in³

• Cube:

Surface Area: \(61.44\) m²
Volume: \(32.768\) m³

• Trailer:

Volume (Space Inside): \(10710\) ft³