SOLUTION: a square has an area of 49 sq cm. what is the area of the inscribed circle? express your answer as a decimal to the nearest tenth

Question 168872: a square has an area of 49 sq cm. what is the area of the inscribed circle? express your answer as a decimal to the nearest tenth
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
a square has an area of 49 sq cm. what is the area of the inscribed circle? express your answer as a decimal to the nearest tenth
.
Draw a diagram of the problem.
Doing so, you will see that the diameter of the circle is equivalent to the diameter of circle. And, we know that half the diameter is the radius.
.
So, if we:
Let x = length of one side of the square (this is also equal to the radius)
.
The problem states that the area of the square is 49 sq cm:
And, we know that area of any square is:
(length of one side)^2
or
x^2 = 49
taking the square root of both sides:
x = 7 cm (this the length of the side of the square and the radius of the circle)
.
Area of circle then:
(pi)r^2
(3.14)(7^2)
(3.14)(49)
153.86
rounding to the nearest tenth:
153.9 sq cm

RELATED QUESTIONS
A circle has an area of 900 pi sq cm. What is the diameter? ?... (answered by richwmiller)

Problem: A regular hexagon is inscribed in a circle with a two-inch radius. What is the (answered by stanbon)

Find the area of a hexagon with a square having an area of 72 sq. cm. inscribed in a... (answered by greenestamps)

a circle has an area of 10(3.14)cm sq. what is the... (answered by Maths68)

a square is inscribed in a circle. If the area of the circle is 25π sq. mm, what is the (answered by Boreal,josmiceli,MathTherapy)

A circle is inscribed inside a square that has an area of 256 in squared. What is the... (answered by Stitch)

A sq of side 5x is inscribed in a circle. Express the area of a circle as a function of... (answered by Fombitz)

the area of a circle is 56 sq cm and the area of square s 32 sq cm . what fraction is the (answered by ikleyn)

a square board has an area of 169 sq. cm. what is the... (answered by Fombitz)