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Intermediate Geometry : Prisms

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1151 : Intermediate Geometry

Find the volume of the regular hexagonal prism.

Possible Answers:

974.28

931.42

944.50

950.02

Correct answer:

974.28

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(5)^2=\frac{75\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{75\sqrt3}{2} \times 15=974.28$

Remember to round to places after the decimal.

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Example Question #38 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

8888.73

9005.92

8822.20

8978.95

Correct answer:

8978.95

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(12)^2=216\sqrt3$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=216\sqrt3 \times 24=8978.95$

Remember to round to places after the decimal.

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Example Question #31 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

440

424

432

448

Correct answer:

432

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{18 \times 4}{2}=36$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=36 \times 12 =432$

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Example Question #32 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

240

360

180

200

Correct answer:

180

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{12 \times 3}{2}=18$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=18\times 10 =180$

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Example Question #61 : Prisms

Find the volume of the prism.

Possible Answers:

2600

2720

2680

2640

Correct answer:

2640

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{30\times 8}{2}=120$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=120\times 22=2640$

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Example Question #62 : Prisms

Find the volume of the prism.

Possible Answers:

230

300

190

170

Correct answer:

300

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{12\times 5}{2}=30$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=30\times 10=300$

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Example Question #63 : Prisms

Find the volume of the prism.

Possible Answers:

888

902

896

908

Correct answer:

896

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{16\times 8}{2}=64$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=64\times 14=896$

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Example Question #1161 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

240

160

200

120

Correct answer:

160

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{4\times10}{2}=20$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=20\times 8=160$

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Example Question #65 : Prisms

Find the volume of the prism.

Possible Answers:

179

198

170

207

Correct answer:

198

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{4\times 11}{2}=22$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=22\times 9=198$

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Example Question #66 : Prisms

Find the volume of the prism.

Possible Answers:

1050

1078

1022

1092

Correct answer:

1050

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{10\times 15}{2}=75$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=75\times 14=1050$

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Intermediate Geometry : Prisms

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1151 : Intermediate Geometry

Example Question #38 : How To Find The Volume Of A Prism

Example Question #31 : How To Find The Volume Of A Prism

Example Question #32 : How To Find The Volume Of A Prism

Example Question #61 : Prisms

Example Question #62 : Prisms

Example Question #63 : Prisms

Example Question #1161 : Intermediate Geometry

Example Question #65 : Prisms

Example Question #66 : Prisms

All Intermediate Geometry Resources

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