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The can s radius is about 1493 inches The volume of a box is 72 cm3 Its height is 3 cm Its length is 15 times its width What are the length and width of the box The formula for the volume of the box is V LWH The volume is 72, the height is 3 and the length is 15 times the width L 1:5W so the formula becomes 72 1:5W W 3 72 1:5W W 3 72 4:5W 2 72 W2 4:5 16 W 2 4 W The box s width is 4 cm and its length is 1:5 4 6 cm The surface area of a ball is 314 square inches What is the ball s diameter The formula for the surface area of a sphere is SA 4r2 The area is 314, so the formula becomes 314 4r2 314 4r2 314 r2 4 r 314 r 4 5%r The radius of the ball is approximately 5 inches The diameter is twice the radius, so the diameter is approximately 10 inches The manufacturer of a six-inch drinking cup is considering increasing its radius The cup has straight sides (the top is the same size as the bot-
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tom) If the radius is increased by one inch, the new volume would be 1696 cubic inches What is the cup s current radius The formula for the volume of a right circular cylinder is V r2 h The cup s height is 6 If the cup s radius is increased, the volume would be 1696 Let x represent the cup s current radius Then the radius of the new cup would be x 1 The volume formula becomes 169:6  x 1 2 6 169:6  x 1 2 6   169:6 169:6 2 x 1 %9 6 6 9 x 1 2 9 x 1 x 1 9 x2 2x 1 0 x2 2x 8 0 x 2 x 4 x 2 0 x 4 0 (This does not lead to a solution) x 2 The cup s current radius is approximately 2 inches
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1 The area of a triangle is 12 in2 The length of its base is two-thirds its height What are the base and height 2 The area of a triangle is 20 cm2 The height is 3 cm more than its base What are the base and height 3 The sum of the base and height of a triangle is 14 inches The area is 20 in2 What are the base and height 4 The hypotenuse of a right triangle is 85 cm long One leg is 71 cm longer than the other What are the lengths of its legs 5 The manufacturer of a food can wants to increase the capacity of one of its cans The can is 5 inches tall and its diameter is 6 inches The manufacturer wants to increase the can s capacity by 50% and wants the can s height to remain 5 inches How much does the diameter need to increase
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6 A pizza restaurant advertises that its large pizza is 20% larger than the competition s large pizza The restaurant s large pizza is 16 inches in diameter What is the diameter of the competition s large pizza
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1 The area formula for a triangle is A 1 BH The area is 12 The 2 length of its base is two-thirds its height, so B 2 H The formula   3 1 2 becomes 12 H H  2 3  1 2 H H 12 2 3 1 2 12 H 2 2 3 1 12 H 2 3 3 12 H 2 36 H 2 6 H The height of the triangle is 6 inches Its base is 2 6 4 inches 3 2 The formula for the area of a triangle is A 1 BH The area is 20 2 The height is 3 cm more than the base, so H B 3 The formula becomes 20 1 B B 3 2 1 20 B B 3 2 2 20 B B 3 40 B B 3 40 B2 3B 0 B2 3B 40 0 B 5 B 8 B 5 0 B 8 0 (This does not lead to a solution) B 5 The triangle s base is 5 cm and its height is 5 3 8 cm