Question

Find the area of the figure shown in the diagram to the nearest hundredth.

A) 157.08 ft2
B) 162.8 ft2
C) 257.08 ft2
D) 414.16 ft2






A sphere of diameter D inches is cut by a plane which passes through its center. Find the area of the cross-section, leaving the answer in terms of π. A) πD

4  in2 B) πD 2  in2 C) πD2 4  in2 D) πD2 2  in2 2)

 Find the area of the figure shown in the diagram to the nearest hundredth. A) 16.00 m2 B) 28.57 m2 C) 41.13 m2 D) 49.12 m 2

Answer 1

area of square=10*10=100
area of circle=pi*d^2/4
=pi*100/4
=25*pi
as we have 4 semi circles means 2 full circles
so tatal area=100+50*pi=257 feet^2
so opton c

Answer 2

Figure 1: The figure has a square and 2 circles. So, to find he area of the figure we will add the area of square plus area of 2 circles.

Now, the side length of square is = 10 feet

Area = 10*10=100 square feet

The side of square acts as a diameter, so radius will be = 10/2 = 5 feet

Area of circle =
`\pi r^(2)`

=
`3.143*5*5=78.575`

Area of 2 circles will be = 78.575*2 = 157.15

So, area of the figure = 100+157.15 = 257.15 square feet.

So, option C is correct.

2. When a sphere is cut by a plane which passes through the center, the cross section is a circle with the same diameter of the sphere.

So, diameter is D. Then radius = D/2

Area of circle =
`\pi ((D)/(2))^(2)` or
`\pi (D^(2) )/(4)` square inches. The given options are not clear(May be 3rd one). But this is the correct answer.