- a.The length of arc BD is a quarter of the circumference of A,
or 16πfeet. - b.A quarter of 360° is 90°; ∠BAD is a right angle.
- c.This question is much simpler than it seems. The half circles
that cap square ABCD form the same area as the circular void in
the center. Find the area of square ABCD, and that is your answer.
12 feet ×12 feet = 144 feet. Choice aand dare the same answer.
Choice bis a negative area and is incorrect.
Set 79
- b.The radii of L and M are half the radius of K. Their areas
equal π(7.5 feet)^2 , or 56.25πsquare feet each. The area of K is
π(15^2 ), or 225πsquare feet. Subtract the areas of circles L and M
from the area of K: 225πsq. ft. – 112.5πsq. ft. = 112.5πsquare
feet. - b.A ratio is a comparison of two quantities, as discussed in chapter
- You’ll need to compare the values for area you found in question
- Though M has half the radius of K, it has a fourth of the
area of K. 56.25πsquare feet: 225.0πsquare feet, or 1:4. - Area = 2,025πsquare feet.You will need to use your mastery of the
Pythagorean theorem to solve for leg OA. Then plug that value into
the area for a circle, as OAis also the radius: a^2 + 60^2 = 75^2. a^2 + 3,600
= 5,625. a^2 = 2,025. a= 45. Then put this radius into A = πr^2 , A = π(45)^2
= 2,025πsquare feet. - 337.5π. Since the area of circle O is 2,025πsquare feet and
m∠AOC = 60º, set up a proportion to calculate the area of the slice
of circle contained by radii OAand OC. Do this by comparing the
part to whole ratio of the angle measurements to the part to whole
ratio of the areas:
wpharotle= 3660 0 ºº= par 2 t 0 ia 2 l 5 aπrea
360 (partial area) = 60(2025π)
partial area = 60(2 306 025 π)= 337.5π
501 Geometry Questions