A circle has an area of 81π in2. Which of the following is the circumference of the circle in terms of pi ( π)?

A. 4.5 π in

B. 14 π in

C. 18 π in

D. 9 π in

Answer Explanation:

we need to find the circumference of the circle from the given area.

The first step is to find the radius of the circle using the given area. Let r be the radius of the circle, then:

Substituting the value of area in the above equation becomes

Dividing both sides by pi and taking square root on both sides yields

Now, we know the radius of circle to be 9 in, the circumference of the circle becomes,

in.

Therefore, the Correct Answer is C.

Q #1: A bucket containing 3 3/5 gallons of water is 2/3 full. How many gallons of water is in one fully filled bucket?

A. 13/15

B. 6 7/15

C. 8 2/5

D. 5 2/5

Answer Explanation

we are asked to find the number of gallons a full tank holds. A full tank is treated as 1 whole.

Letting x be the number of gallons in full tank and setting the proportion equation with the number of gallons on the numerator and fraction of tank on denominator as follows.

Convert the mixed fraction into proper fraction and cross-multiply to find the value of x.

x 1 full tank=185 gallons23full tank

A full tank holds 27/5 gallons, which when converted to a mixed fraction is 5 2/5.
Q #2: The length of a rectangular room is 2 feet greater than its width. Which of the following equations represents the area (A) of the room?

A. A = 2x

B. A = 2x+2(x+2)

C. A = x+(x+2)

D. A = x(x+2)

Answer Explanation

we are asked to find the area of a rectangle, which can only be found by finding the relation between length and width. Now, letting x represent the width, then

Length of rectangle=(x+2)

Width of the rectangle= x

Area of the rectangle, A= Length*width=(x+2)*x

A=x(x+2)

Therefore, the area of the rectangle becomes x(x+2).
Q #3: Simplify the expression above. Which of the following is correct?

A. 6

B. 18

C. 9

D. 22

Answer Explanation

To simplify this expression, we follow the order of operations as follows:

First, we start with the numerator and solve it as follows

[2(6+3*9)]

We start with multiplication in inner brackets, 3 * 9 = 27. The expression becomes

[2(6+27)]

Then, we carry out the addition of 6+27=33. Then, the expression yields

[2(33)]=2*33=66

Now, we solve for denominator, which is 6/2=3.

Thus, the expression is reduced into

The expression reduces into 22.