Question

Please help me, this question is so confusing and I tried almost every way to solve this and it’s still wrong. It wants me to find how much metal need to make the 16 cans and I tried multiplying 16 and it’s still wrong. Please help! Diameter is 8, height is 9. Please use 3 as pi to solve.

Answer 1

`4992 \text{ cm}^2`

Explanation:

We can model the amount of metal, in square centimeters, that is needed to make a soup can with the expression:

`(2 \cdot \text{area of base}) + (\text{area of side})`

We can first solve for the surface area of a soup can, using the fact that its bases are circles.

`A_{\text{circle}} = \pi r^2`

↓ substituting 3 for π

`A_{\text{base}} = 3r^2`

↓ plugging in radius (which is 1/2 of diameter, given as 8)

`A_{\text{base}} = 3(4)^2`

↓ simplifying

`A_{\text{base}} = 48 \text{ cm}^2`

Then, we can solve for the area of its side, which we can think of as an elongated circumference (circumference multiplied by height).

`A_{\text{circumference}} = \pi d`

`A_{\text{side}} = h(\pi d)`

↓ substituting 3 for π

`A_{\text{side}} = h(3d)`

↓ plugging in height and diameter

`A_{\text{side}} = 9(3 \cdot 8)`

↓ simplifying

`A_{\text{side}} = 216 \text{ cm}^2`

Next, we can solve for the surface area of one soup can.

`(2 \cdot \text{area of base}) + (\text{area of side})`

↓ plugging in solved values

`(2 \cdot 48 \text{ cm}^2) + 216 \text{ cm}^2`

↓ simplifying

`96 \text{ cm}^2 + 216 \text{ cm}^2`

↓ performing addition

`312 \text{ cm}^2`

Finally, we can solve for the amount of metal needed for 16 cans by multiplying the amount for 1 can by 16.

`16 \cdot 312 \text{ cm}^2`

↓ performing multiplication

`\boxed{4992 \text{ cm}^2}`