Answered

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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?

Sagot :

mathstudent55

Answer:

1.243 cm

Step-by-step explanation:

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

[tex] SA = 2\pi r^2 + 2 \pi rh [/tex]

[tex] SA = 2\pi r(r + h) [/tex]

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.

[tex] SA = 2\pi r(r + h) [/tex]

[tex] 2\pi r(r + h) = SA [/tex]

[tex] r + h = \dfrac{SA}{2\pi r} [/tex]

[tex] h = \dfrac{SA}{2\pi r} - r [/tex]

[tex] h = \dfrac{104.3~cm^2}{2(3.14159)(3.5~cm)} - 3.5~cm [/tex]

[tex] h = 1.243~cm [/tex]

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