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Name: _______________________________________________________________________________ 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.