Category 2
Geometry
Meet #4 February 2007 – Practice #1
1) How many centimeters are in the circumference of a circle with area 78.5 cm2. Use 3.14 for and round to the nearest tenth.
2) How many inches are in the circumference of a circle with area 177 in2. Use 3.14 for and round to the nearest whole number.
3) How many square feet are in the area of a circle with circumference of 94 feet? Use 3.14 for and round to the nearest whole number.
4) How many square feet are in the area of a circle with circumference of 56 feet? Use 3.14 for and round to the nearest whole number.
5) A circle is inscribed in a square with area 144 m2. How many square meters are in the circumference of the circle? Use 3.14 for and express your answer as a decimal to the nearest hundredth.
6) A bicycle has tires with radius 18 inches. If the bicycle travels 942.5 feet how many revolutions have the tires made? Use 3.14 for and round to the nearest whole number.
7) If a sphere with diameter of 12 cm rolls down a hill making 40 revolutions, how far will the center of the sphere have traveled? Use 3.14 for and round to the nearest tenth.
8) The circumference of circle A is 12 feet and the circumference of circle B is 30 feet. What is the ratio of the area of circle A to the area of circle B? Express your answer as a common fraction?
Category 2
Geometry
Meet #4 February 2007 – Practice #1
1) How many centimeters are in the circumference of a circle with area 78.5 cm2. Use 3.14 for and round to the nearest tenth.
*A= r2 = 3.14r2 = 78.5 divide both sides by 3.14 to get r2 = 25 and so r = 5. The circumference = 2r = 2(3.14)(5) = 31.4
2) How many inches are in the circumference of a circle with area 177 in2. Use 3.14 for and round to the nearest whole number.
*A= r2 = 3.14r2 = 177 divide both sides by 3.14 to get r2 and so r . The circumference = 2r = 2(3.14)(7.508) 47.15 47
3) How many square feet are in the area of a circle with circumference of 94 feet? Use 3.14 for and round to the nearest whole number.
*C= 2r = 2(3.14)r = 94 divide both sides by 3.14 to get 2r and so r . The Area = r2 = 3.14r2 (3.14)(14.968)2 703.488703
4) How many square feet are in the area of a circle with circumference of 56 feet? Use 3.14 for and round to the nearest whole number.
*C= 2r = 2(3.14)r = 56 divide both sides by 3.14 to get 2r and so r . The Area = r2 = 3.14r2 (3.14)(8.917)2 249.682250
5) A circle is inscribed in a square with area 144 m2. How many square meters are in the circumference of the circle? Use 3.14 for and express your answer as a decimal to the nearest hundredth.
*The Area of the square = the side squared. So s2 = 144 and s = 12. The diameter of the inscribed circle is the same as the side length of the square, so d = 12 and radius = 6. The circumference is C= 2r = 2(3.14)r = 2(3.14)(6) = 37.68
6) A bicycle has tires with radius 18 inches. If the bicycle travels 942.5 feet how many revolutions have the tires made? Use 3.14 for and round to the nearest whole number.
*The tire radius is 18 inches. The Circumference of the tire = 2r = 2(3.14)r = 2(3.14)(18) = 113.04 so the bike would travel 113.04 inches each revolution. 942.5 feet = 942.5x12 = 11310 inches. The number of revolutions would then be 11310 113.04 100.05 100 revolutions
7) If a sphere with diameter of 12 cm rolls down a hill making 40 revolutions, how far will the center of the sphere have traveled? Use 3.14 for and round to the nearest tenth.
*C = 2r = d = 3.14(12) = 37.68. So each revolution the whole sphere travels 37.68 cm. So in 40 revolutions the center of the sphere will travel (37.68)(40) = 1507.2
8) The circumference of circle A is 12 feet and the circumference of circle B is 30 feet. What is the ratio of the area of circle A to the area of circle B? Express your answer as a common fraction?
*You don't actually need to know the radii or diameters to answer this question. If you find the ratio of the two circumferences 12:30 which simplifies to 2:5 you can say that the ratio of the radii is also 2:5 since radius and circumference are both measured in the same units(linear units or units to the first power). To find the ratio of the areas you need to square the ratio of the radii since area is measured in square units!!! So the ratio of the areas is 22: 52 = 4 : 25 =