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12.07 Problem Solving with Surface Area and Volume

On the problems below, show all of your work for full credit.

1. A storage silo is in the shape of a cylinder with a hemisphere at the top. The total height of the silo is 35 ft. The circumference of the cylinder is 22 ft.

a) Find the radius of the silo.

Hint: You can find the radius of a circle when given the circumference. Use C = 2πr and solve for r.

r =      ft.

Show your work below

b) Find the height of the cylindrical portion of the silo.

Hint: Now that you know the radius of the hemisphere, you can find the height of the cylinder, by Total Height of Silo – Height of Hemisphere

h =      ft.

Show your work below

c) Find the volume of the cylindrical portion of the silo.

Hint: Use the formula for the volume of a cylinder

V =      ft.3

Show your work below

d) Find the volume of the hemispherical portion of the silo.

Hint: Use the formula for the volume of a sphere, then divide it by 2.

V =      ft.3

Show your work below

e) What is the total volume of the silo?

Hint: Add the two volumes together

V =      ft.3

Show your work below

2. Joe is making a toy from a rectangular block of wood. He drills two holes, each with diameter 1.4 cm, through the block. The block of wood has length 15 cm, width 8 cm, and height 5 cm.

Hint: Look back at YOUR TURN #1

a) What is the volume of the block before the holes are drilled?

V =      cm3

Show your work below

b) What is total volume removed by the drilled holes?

V =      cm3

Show your work below

c) What is the volume of the block after the holes are drilled?

V =      cm3

Show your work below

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