Question

in 8 - 10, apply the formula for surface area of a cylinder $sa = 2b + ph$.

1. a new cylindrical can with a diameter of 5 cm is being designed by a local company. the surface area of the can is 150 square centimeters. what is the height of the can? estimate using 3.14 for $pi$, and round to the nearest hundredth.

Explanation:

Step1: Find radius of the can

The diameter is 5 cm, so radius $r = \frac{5}{2} = 2.5$ cm.

Step2: Calculate base area $B$

Base area is a circle: $B = \pi r^2 = 3.14 \times (2.5)^2 = 3.14 \times 6.25 = 19.625$ cm².

Step3: Calculate perimeter $P$ of base

Perimeter (circumference) $P = 2\pi r = 2 \times 3.14 \times 2.5 = 15.7$ cm.

Step4: Rearrange surface area formula for $h$

Given $SA = 2B + Ph$, solve for $h$:
$Ph = SA - 2B$
$h = \frac{SA - 2B}{P}$

Step5: Substitute values to find $h$

$h = \frac{150 - 2 \times 19.625}{15.7} = \frac{150 - 39.25}{15.7} = \frac{110.75}{15.7} \approx 7.0541$

Step6: Round to nearest hundredth

Round 7.0541 to two decimal places: 7.05

Answer:

The height of the can is $\boldsymbol{7.05}$ centimeters.