Question

A can of tomato soup has a circular base with a diameter of 7 cm. If the surface area of the can is 104.3 cm. What is the height of the can?

Answer 1

1.243 cm

Explanation:

The surface area of a cylinder is the sum of the area of the two congruent circular bases and the rectangular lateral area.

`SA = 2\pi r^2 + 2 \pi rh`

`SA = 2\pi r(r + h)`

We are given the surface area and the diameter.

r = d/2 = 7 cm / 2 = 3.5 cm

We can solve for h, the height.

`SA = 2\pi r(r + h)`

`2\pi r(r + h) = SA`

`r + h = (SA)/(2\pi r)`

`h = (SA)/(2\pi r) - r`

`h = (104.3~cm^2)/(2(3.14159)(3.5~cm)) - 3.5~cm`

`h = 1.243~cm`