Question

determine the amount of steel needed for the can of tomato paste. use the π button on the calculator. round to the nearest tenth of a unit. the surface area of the can is approximately 3.8 in 1.1 in

Explanation:

Step1: Identify can as cylinder

A can is a cylinder. The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$. Given diameter $d = 3.8$ in, so radius $r=\frac{d}{2}=\frac{3.8}{2}=1.9$ in and height $h = 4.1$ in.

Step2: Calculate area of two bases

The area of one base is $A_{base}=\pi r^2$. For two bases, $A_{2bases}=2\pi r^2=2\pi(1.9)^2=2\pi\times3.61\approx2\times3.14\times3.61 = 22.6708$ in².

Step3: Calculate lateral - surface area

The lateral - surface area formula is $A_{lateral}=2\pi rh$. Substitute $r = 1.9$ in and $h = 4.1$ in, we get $A_{lateral}=2\pi\times1.9\times4.1=2\pi\times7.79\approx2\times3.14\times7.79 = 48.9812$ in².

Step4: Calculate total surface area

$S=A_{2bases}+A_{lateral}=22.6708 + 48.9812=71.652\approx71.7$ in².

Answer:

$71.7$ in²