A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches (in). The volume of the dictionary will be 216in^(3). What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

Question

A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches (in). The volume of the dictionary will be  216in^(3). What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

Bytelearn · Accepted Answer

Understanding the relationship: Understand the relationship between volume, area, and thickness in a rectangular prism. The volume (V) of a rectangular prism can be found by multiplying the area (A) of the base (or front cover in this case) by the thickness (t) of the prism. The formula is V = A * t.Solving for the area: Given the volume and thickness, solve for the area of the front cover. We are given the volume V = 216 in^3 and the thickness t = 3 in. Using the formula from Step 1, we can solve for A: A = V / t.Calculating the area: Calculate the area of the front cover. Substitute the given values into the equation: A = 216 in^3 / 3 in. A = 72 in^2.Verifying the calculation: Verify the calculation to ensure there are no math errors. Double-check the division: 216 divided by 3 equals 72. No math errors are present in the calculation.

A new dictionary in the shape of a rectangular prism will have a thickness of $3$ inches (in). The volume of the dictionary will be $216 \mathrm{in}^{3}$ . What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

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A new dictionary in the shape of a rectangular prism will have a thickness of $3$ inches (in). The volume of the dictionary will be $216 \mathrm{in}^{3}$ . What must be the area of the front cover, a face perpendicular to the thickness, in square inches?