Download Working Backwards- Volume and Surface Area

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Working Backwards- Volume and Surface Area
Example #1: The volume of a cone with a 30 mm radius is 9420 mm3. What is the height of the cone to
the nearest millimeter?
1
3
B = Area of the base
V= Bh
A = Πr2
1
3
9420 = B h
A = Π(30)2
1
3
9420 = (2827.4) h
A = 2827.4 mm2
10 = h
Example #2: Find the height of the cylinder.
V=Bh
B = Area of the base
112 Π = B ∙ h
A = Πr2
112 Π = 16 Π ∙ h
A = Π(4)2
112
16
=h
A = 16 Π
7=h
Example #4: Find the width of a rectangular solid with length 15 cm, height 8 cm, and lateral area of 400 cm2.
Draw and Label
SL = P h
400 = P h
400 = 46 h
8 cm
15 cm
?
8.7 = h
P = 8 +8 +15 + 15
P = 46
1.
Cone- volume: 36 cubic inches; height: 9
inches
2. The volume of a cylinder is 441 in3. The height of the
cylinder is 9 in. Calculate the radius of the cylinder to
the nearest tenth of a centimeter.
3. If the volume of a cone is 10 what is its height
if the area of the base is 10 m2 ?
4. Solve for x when the surface area is 298 ft2.
5. The surface area of a cylinder is 48 square
feet. The radius of the cylinder is 3 feet. What
is the height of the cylinder?
6. Find the value of x when S = 200 ft2
7. The volume of a cylinder is 794.3 cm3. The height of
the cylinder is 7 cm. Calculate the radius of the
cylinder to the nearest tenth of a centimeter.
8. Cone- volume: 238 cubic centimeters; height: 74
centimeters
9. The lateral area for a regular triangular prism
measures 462 inches2. Calculate the surface area of
the prism if the height of the prism measures 11 inches.
10. The volume of a cylinder is 3600Π cm3 and the height is 16
cm. Find the radius.