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High School Math : Geometry

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Example Questions

Example Question #2 : How To Find The Volume Of A Prism

Find the volume of the following triangular prism:

Triangular_prism

Possible Answers:

$128\sqrt{3}m^3$

$98\sqrt{3}m^3$

$88\sqrt{3}m^3$

$118\sqrt{3}m^3$

$108\sqrt{3}m^3$

Correct answer:

$108\sqrt{3}m^3$

Explanation:

The formula for the volume of an equilateral, triangular prism is:

V = (base)(height)

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

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Example Question #1 : How To Find The Volume Of A Prism

What is the volume?

Question_5

Possible Answers:

Correct answer:

Explanation:

The volume is calculated using the equation:

V=lwh

V=(2)(4)(6)=48

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Example Question #1 : How To Find The Volume Of A Prism

A rectangular box has two sides with the following lengths:

3$ cm$ and 4 $ cm$

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Possible Answers:

Correct answer:

Explanation:

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

84=12x

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

x=7

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

A=28

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Example Question #1 : How To Find The Surface Area Of A Cylinder

This figure is a right cylinder with radius of 2 m and a height of 10 m.

What is the surface area of the right cylinder (m²)?

Possible Answers:

150.80

62.83

25.14

125.71

125.66

Correct answer:

150.80

Explanation:

In order to find the surface area of a right cylinder you must find the area of both bases (the circles on either end) and add them to the lateral surface area. The area of the two circles is easy to find with but remember to multiply by 2 for both bases

$2\cdot2^{2}\cdot\pi= 25.14$ .

Next find the lateral area. The lateral area if unrounded would be a rectangle with height of 10 m and length equal to the circumference of the base circles. Thus the lateral area is

$4\cdot\pi\cdot10= 125.66$

Now add the lateral area to the area of the two bases:

25.14 +125.66=150.80

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Example Question #2 : How To Find The Surface Area Of A Cylinder

Find the surface area of a cylinder given that its radius is 2 and its height is 3.2.

Possible Answers:

$12.8\pi$

$20.8\pi$

$8\pi$

20.8

Correct answer:

$20.8\pi$

Explanation:

The standard equation to find the surface area of a cylinder is

$Surface\ Area=2\pi r^2+2\pi rh$

where denotes the radius and denotes the height.

Plug in the given values for and to find the area of the cylinder:

$Area=2\pi (2)^2+2\pi (2)(3.2)=8\pi +12.8\pi =20.8\pi$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

The base of a cylinder has an area of $9\pi$ and the cylinder has a height of . What is the surface area of this cylinder?

Possible Answers:

$90\pi$

$18\pi$

$72\pi$

Correct answer:

$90\pi$

Explanation:

The standard equation for the surface area of a cylinder is

$SA=2\pi r^2+2\pi rh$

where denotes radius and denotes height. We've been given the height in the question, so all we're missing is the radius. However, we are able to find the radius from the area of the circle:

$Area=\pi r^2$

We know the area is $9\pi$

$9\pi =\pi r^2$ so r=3

Now that we have both and , we can plug them into the standard equation for the surface area of a cylinder:

$SA=2\pi (3)^2+2\pi (3)(12)=18\pi +72\pi =90\pi$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following cylinder.

Cylinder

Possible Answers:

$246 \pi m^2$

$252 \pi m^2$

$260 \pi m^2$

$240 \pi m^2$

$256 \pi m^2$

Correct answer:

$252 \pi m^2$

Explanation:

The formula for the surface area of a cylinder is:

$SA = lateral\ area + 2\cdot (base)$

$SA = 2 \pi r (h) + 2 (\pi r^2)$

where is the radius of the base and is the length of the height.

Plugging in our values, we get:

$SA = 2 \pi (7m) (11m) + 2 \pi (7m)^2$

$SA = 154 \pi m^2 + 98 \pi m^2 = 252 \pi m^2$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following cylinder.

Cylinder

Possible Answers:

$114 \pi m^2$

$104 \pi m^2$

$124 \pi m^2$

$94 \pi m^2$

$84 \pi m^2$

Correct answer:

$104 \pi m^2$

Explanation:

The formula for the surface area of a cylinder is:

SA = 2(base)+(circumference)(height)

$SA = 2(\pi r^2)+(2 \pi r h)$

Where is the radius of the cylinder and is the height of the cylinder

Plugging in our values, we get:

$SA = 2\pi (4m)^2 + 2 \pi (4m)(9m)$

$SA = 104 \pi m^2$

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Example Question #2 : Cylinders

Find the surface area of the following partial cylinder.

Cylinder_sector

Possible Answers:

$\frac{104 \pi m^2}{3} + 80m^2$

$\frac{80 \pi m^2}{3} + 144m^2$

$144 \pi m^2+ 80m^2$

$\frac{144 \pi m^2}{6} + 80m^2$

$\frac{144 \pi m^2}{2} + 80m^2$

Correct answer:

$\frac{104 \pi m^2}{3} + 80m^2$

Explanation:

The formula for the surface area of this partial cylinder is:

SA = 2(base)(part)+2(face)+(circumference)(part)(height)

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

Where is the radius of the cylinder, is the height of the cylinder, and part is the sector of the cylinder.

Plugging in our values, we get:

$SA = 2(\pi (8m)^2)\left(\frac{60}{360}\right)+2(8m)(5m)+(2 \pi (8m))\left(\frac{60}{360}\right)(5m)$

$SA = \frac{64 \pi m^2}{3} + 80m^2 + \frac{40 \pi m^2}{3}$

$SA = \frac{104 \pi m^2}{3} + 80m^2$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following partial cylinder.

Partial_cylinder

Possible Answers:

$200 \pi m^2 + 240m^2$

$234 \pi m^2 + 234m^2$

$240 \pi m^2 + 240m^2$

$234 \pi m^2 + 200m^2$

$234 \pi m^2 + 240m^2$

Correct answer:

$234 \pi m^2 + 240m^2$

Explanation:

The formula for the surface area of this partial cylinder is:

SA = 2(base)(part)+2(face)+(circumference)(part)(height)

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

where is the radius of the cylinder, is the height of the cylinder, and part is the sector of the cylinder.

Plugging in our values, we get:

$SA = 2(\pi r^2)(part)+2(r)(h)+(2 \pi r)(part)(h)$

$SA = 2(\pi (6m)^2)\left(\frac{270}{360}\right)+2(6m)(20m)+(2\pi (6m))\left(\frac{270}{360}\right)(20m)$

$SA = 54 \pi m^2 + 240m^2 +180 \pi m^2$

$SA = 234 \pi m^2 + 240m^2$

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High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : How To Find The Volume Of A Prism

Example Question #1 : How To Find The Volume Of A Prism

Example Question #1 : How To Find The Volume Of A Prism

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #2 : How To Find The Surface Area Of A Cylinder

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #2 : Cylinders

Example Question #1 : How To Find The Surface Area Of A Cylinder

All High School Math Resources

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