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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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