Answers
Set 78
- b.The perimeter of a circle is twice the radius times pi: (2 × 57
inches)π. - d.You first need to divide the given diameter of 206 feet, in two in
order to find the radius. The area of a circle is the radius squared
times pi: π(103 feet)^2. - a.Follow the same first step as you did in question 369. Since
ME= 10x, the radius is 5x. Area = π(5x)^2 = π(25x^2 ) = 25x^2 π - c.If the area of a square is 484 square feet, then the sides of the
square must measure 22 feet each. The diameter of an inscribed
circle has the same length as one side of the square. The maximum
area of an inscribed circle is π(11 feet)^2 , or 121πsquare feet. - b.Backsolve by plugging the given circumference, 192πfeet, into
the formula for circumference of a circle. The circumference of a
circle is pitimes twice the radius. 192 feet is twice the length of the
radius; therefore half of 192 feet, or 96 feet, is the actual length of
the radius. - a.Just as in question 372, backsolve by plugging 289πinto the
formula for area. The area of a circle is pitimes the square of its
radius. If 289 feet is the square of the circle’s radius, then 17 feet is
the length of its radius. Choice cis not the answer because 144.5 is
half of 289, not the square root of 289. - d.Have you forgotten these terms? Look back to chapter 13 on
polygons for a refresher. In the mean time, don’t get too distracted
by the shape of the polygon, in this case a dodecagon. Hold fast to
two facts—the circle is set within the dodecagon and the apothem
goes to the dodecagon’s center. Therefore, the center of the circle
overlaps with the center of the dodecagon and, accordingly, the
apothem = the radius. From here, solve for area. A = πr^2. A = π(13)^2.
A = 169πsquare meters.
501 Geometry Questions