Question

3. Calculate the cost of manufacturing this cereal box if cardboard costs $0.01 per square inch 2 points) $1.44 $ 0.75 $ 3.00 $ 2.86 $ 2.16 4. A spherical container is designed to hold as much volume as the rectangular prism above . Its radius is 3.7 in . Find the surface area of the sphere rounded to the nearest square inch. (2 points) 141 square inches 128 square inches 216 square inches 172 square inches

Answer 1

To calculate the cost of manufacturing the cereal box, we first need to find the surface area of the rectangular prism.

The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh

Given:
Length (l) = 6 inches
Width (w) = 3 inches
Height (h) = 4 inches

Surface Area = 2(6*3) + 2(6*4) + 2(3*4)
Surface Area = 2(18) + 2(24) + 2(12)
Surface Area = 36 + 48 + 24
Surface Area = 108 square inches

Now, we can calculate the cost of manufacturing the cereal box:
Cost = Surface Area * Cost per square inch
Cost = 108 * $0.01
Cost = $1.08

Therefore, the cost of manufacturing the cereal box is $1.08.

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The surface area of a sphere is given by the formula:
Surface Area = 4πr^2

Given:
Radius (r) = 3.7 inches

Surface Area = 4π(3.7)^2
Surface Area ≈ 4*3.14*(13.69)
Surface Area ≈ 4* 3.14 * 13.69
Surface Area ≈ 171.51 square inches

Rounded to the nearest square inch, the surface area of the sphere is 172 square inches.