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?

Question

asked Oct 10, 2022 82.1k views

1 Answer

Evanss · Answer 1 · 2022-10-14T19:01:22+0000

Answer:

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