Question 1

We are given that the object is composed of a cone on top of a cylinder. We can use the Pythagorean relationship to find the slant height of the cone.

s 2 = 5 2 + 7 2 = 25 + 49 = 74 s = 74

Slant height = 74

Then we can use the formula for the surface of a cone, exculding the bottom ( S A cone =πrs ) .

For the cylindrical part of the object, we can use the formula for the surface area of a cylinder, but only include one circle, the base ( SA cylinder =π r 2 +2πrh ) .

The total surface area can now be calculated:

SA Total =πrs+π r 2 +2πrh =π( 5 ) 74 +π ( 5 ) 2 +2π( 5 )( 8 ) 464.99

Therefore the surface area is approximately 465 cm 2 .

To convert the answer to square inches, use 1 cm = 0.3937 in., so 1 cm 2 = (0.3937) 2 in. 2 .

465 (0.3937) 2 = 72.074855

Therefore the surface area is approximately 72 in 2 .

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