Tagged: ,

• Creator
Topic
• #15019
Keymaster
Post count: 678

Find the shaded area.

Outer square area = 300 × 300

= 90,000mm2

The four quadrants that have been cut out will form a circle with radius 100mm.
Area of circle = π × 1002

= 31,415.93mm2

Shaded area = 90,000 – 31,415.93

= 58,584.07mm2

• Author
Replies
Keymaster
Post count: 678

A circle with radius of 6cm is inscribed in a circle as shown in the diagram. which expression represents the shaded region?
a. $$\pi\times 12^2 – 12^2$$
b. $$\pi\times 6^2 – 12^2$$
c. $$\pi\times 6^2 – 6^2$$
d. $$\pi\times 6^2 – 12\times 6$$

first we need to find the base and height of the square, using Pythagoras. Let each side be x and the hypotenuse will be 12cm (as the radius is 6cm, so the diameter will be 12 which is the hypotenuse)

x2 + x2 = 122

2x2 = 144

x2 = 72

The area of the square will be: A = x × x = x2
∴ A = 72cm2

Area of the circle = π × 62
Shaded area = circle – square

= π × 62 – 72

since 6 × 12 = 72, D is the correct answer

D