Problem |
Solution |
1) Find the area of the S shaped figure. Give an exact answer, so express your answer in terms of
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- The figure consists of 2 3⁄4 circles = 3⁄2 circle
- So the area of the total figure is:
3⁄2 x 222 =
726 sq. mm.
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2) An ice cream cone is a right circular cone. The volume of a right circular cone is 1/3 the volume of the cylinder that has the same radius and height. A small cone has radius 1 inch and height 4 inches. A large cone has double the radius and double the height, so 2 inch radius and 8 inch height. What is a good estimate for the scale factor giving the change in volume of ice cream the large cone can hold compared to the small cone?
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- Small cone volume: 1⁄3 x 4
- Large cone volume: 1⁄3 x 8 x 4
- Scale factor = 32/4 = 8
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3) The triangle has a base of 5 and a height of 12. A rectangle is formed with the same base as the triangle and with the height the length of the hypotenuse of the triangle. What is the area of the rectangle?
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- By the pythagorean theorem:
h =
√
5 2 +
12 2 = √169 = 13 cm.
- Area of the rectangle = 13x5 = 65 sq. cm.
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