Question

example 2
this cylindrical coffee cup is made out of plastic. it is 5 inches tall and has a radius of 1.75 inches.
① how many square inches of plastic were used to make the cup?
② how much coffee can the cup hold?

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \( V \) of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Identify the values of \( r \) and \( h \)

From the problem, the radius \( r = 1.75 \) inches and the height \( h = 5 \) inches.

Step3: Substitute the values into the formula

Substitute \( r = 1.75 \) and \( h = 5 \) into the formula:
\[
V = \pi \times (1.75)^2 \times 5
\]

Step4: Calculate \( (1.75)^2 \)

First, calculate \( (1.75)^2 = 3.0625 \).

Step5: Multiply the values

Now, multiply \( 3.0625 \) by \( 5 \): \( 3.0625 \times 5 = 15.3125 \). Then multiply by \( \pi \) (using \( \pi \approx 3.1416 \)):
\[
V \approx 3.1416 \times 15.3125 \approx 48.08
\]

Answer:

The coffee cup can hold approximately \( 48.08 \) cubic inches of coffee.