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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #151 : Area

Units = cm

Diameter is 22, find the area of the circle.

Possible Answers:

$\small 412cm^{2}$

$\small 400cm^{2}$

$\small 379.94cm^{2}$

$\small 372.94cm^{2}$

Correct answer:

$\small 379.94cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the diameter of the circle, meaning the radius is half of this.

To solve for the area, we just plug it into our equation:

$r=\frac{1}{2}d\rightarrow r=\frac{1}{2}22=11$

$\\A=\small \small \small \small \small \small \small \small \small \pi(11)^{2} \\A= 11\times11\times \pi \\A= 121\pi \\A= 121\times 3.14\\A=379.94cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small \small \small \small 379.94cm^{2}$ .

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Example Question #152 : Area

Units = cm

Diameter is 60, find the area of the circle.

Possible Answers:

$\small 226cm^{2}$

$\small 2628cm^{2}$

$\small 2622cm^{2}$

$\small 2826cm^{2}$

Correct answer:

$\small 2826cm^{2}$

Explanation:

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the diameter of the circle, meaning the radius is half of this.

To solve for the area, we just plug it into our equation:

$r=\frac{1}{2}d\rightarrow r=\frac{1}{2}60=30$

$\\A= \pi(30)^{2} \\A= 30\times30\times \pi \\A= 900\pi \\A= 900\times 3.14\\A= 2826cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small \small \small \small \small 2826cm^{2}$ .

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Example Question #34 : Area Of A Circle

A circle has diameter 12.

What is the area of the circle?

Possible Answers:

$\ 36\pi$

$12\pi$

144

$144\pi$

Correct answer:

$\ 36\pi$

Explanation:

The equation for area of a circle is $A=\pi*r^2$ where r is the radius.

The diameter is twice the length of the radius; therefore, r=6

Squaring 6 gives you 36 which multiplied by pi gives you $36\pi$

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Example Question #35 : Area Of A Circle

The diameter of a circle is 15m . What is the area of this circle?

Possible Answers:

$225\pi$

$125\pi$

$15\pi$

$56.25\pi$

$76.25\pi$

Correct answer:

$56.25\pi$

Explanation:

The formula for area of a circle is:

$A = \pi r^{2}$

We are given the diameter, and the radius $\left ( r\right )$ is half of the diameter.

$r = \frac{1}{2}d$

$r = \frac{1}{2}\left ( 15m\right )$

r = 7.5m

Plug this in to the formula:

$A = \pi \left ( 7.5\right )^{2}$

$A = 56.25\pi$

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Example Question #38 : Area Of A Circle

Find the area of a circle with a diameter of 15.

Possible Answers:

$30\pi$

$\frac{225}{4}$

$\frac{15}{2}\pi$

$\frac{225}{4}\pi$

$225\pi$

Correct answer:

$\frac{225}{4}\pi$

Explanation:

Write the area of a circle.

$A=\pi r^2$

To obtain the radius, divide the diameter by two.

$r=\frac{d}{2} = \frac{15}{2}$

Substitute the radius into the area equation and solve.

$A=\pi( \frac{15}{2})^2 = \frac{225}{4}\pi$

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Example Question #36 : Area Of A Circle

What is the area of a circle with a radius of ?

Possible Answers:

$225\pi$

$15\pi$

$900\pi$

$450\pi$

$30\pi$

Correct answer:

$225\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius and solve for area.

$A=\pi (15)^2 = 225\pi$

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Example Question #40 : Area Of A Circle

The lateral surface area of a cylinder is 25in^2 . What is the total surface area of the cylinder if the top of the cylinder has a radius of 7.85 in ?

Possible Answers:

SA=241in^2

SA=142in^2

None of the other answers.

SA=214in^2

SA=412in^2

Correct answer:

SA=412in^2

Explanation:

If we know the lateral area of our supposed cylinder we need only add the area of the two circles at each end.

Compute the area of one circle:

$A=\pi r^2=\pi (7.85in)^2=193.5in^2$

We multiply by 2 for both ends of the cylinder and add the lateral surface area given to get a total SA of 412in^2 . Keep in mind this is not a real cylinder. The lateral surface area of right cylinder that has a radius of 7.85 might be much larger than 25in^2 . Since we do not know the height we cannot say definitively. However, the process of finding the total surface area if given the lateral surface area remains the same.

$SA=2\cdot 193.5+25=412in^2$

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Example Question #41 : Area Of A Circle

What is the area of a circle with a diameter of one unit?

Possible Answers:

$\frac{3}{2}\pi$

$\frac{1}{4}\pi$

$2\pi$

$\frac{1}{2}\pi$

$\pi$

Correct answer:

$\frac{1}{4}\pi$

Explanation:

Write the area of a circle.

$A=\pi r^2$

Since we are given the diameter of the circle and the area equation calls for the radius, we will need to calculate the radius first.

Divide the diameter by two to get the radius.

$r=\frac{D}{2}= \frac{1}{2}$

$A=\pi \left(\frac{1}{2}\right)^2 = \frac{1}{4}\pi$

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Example Question #155 : Area

Find the area of a circle with a circumference of .

Possible Answers:

$\pi$

$\frac{1}{4}$

$\frac{1}{2\pi}$

$\frac{1}{4\pi}$

$2\pi$

Correct answer:

$\frac{1}{4\pi}$

Explanation:

Write the circumference formula for the circle.

$C=2\pi r$

Substitute the circumference and solve for the radius.

$1=2\pi r$

$r=\frac{1}{2\pi}$

Write the formula for the area of the circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (\frac{1}{2\pi})^2 = \pi(\frac{1}{4\pi^2}) = \frac{1}{4\pi}$

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Example Question #156 : Area

Find the area of a circle with a diameter of 1.8 .

Possible Answers:

$0.81 \pi$

$1.62\pi$

$0.42\pi$

$3.24\pi$

$3.6\pi$

Correct answer:

$0.81 \pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Given the diameter, we will need to divide this by two to obtain the radius.

$r=\frac{d}{2}= \frac{1.8}{2} = 0.9$

Substitute the radius and solve.

$A=\pi (0.9)^2 = 0.81 \pi$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #151 : Area

Example Question #152 : Area

Example Question #34 : Area Of A Circle

Example Question #35 : Area Of A Circle

Example Question #38 : Area Of A Circle

Example Question #36 : Area Of A Circle

Example Question #40 : Area Of A Circle

Example Question #41 : Area Of A Circle

Example Question #155 : Area

Example Question #156 : Area

All Pre-Algebra Resources

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