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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #191 : Solid Geometry

Find the volume of the regular hexagonal prism.

Possible Answers:

394.56

389.71

401.67

387.82

Correct answer:

389.71

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.

$\text{Volume of Prism}=\frac{75\sqrt3}{2} \times 6=389.71$

Remember to round to places after the decimal.

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

Find the volume of the regular hexagonal prism.

Possible Answers:

9.47

11.56

10.39

8.01

Correct answer:

10.39

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.

$\text{Area of Base}=\frac{3\sqrt3}{2}(1)^2=\frac{3\sqrt3}{2}$

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

$\text{Volume of Prism}=\frac{3\sqrt3}{2} \times 4=10.39$

Remember to round to places after the decimal.

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Example Question #36 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

4590.02

4667.35

4416.73

4809.44

Correct answer:

4416.73

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.

$\text{Area of Base}=\frac{3\sqrt3}{2}(10)^2=150\sqrt3$

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

$\text{Volume of Prism}=150\sqrt3\times 17=4416.73$

Remember to round to places after the decimal.

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Example Question #37 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

950.02

944.50

974.28

931.42

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.

Report an Error

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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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #191 : Solid Geometry

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

Example Question #36 : How To Find The Volume Of A Prism

Example Question #37 : How To Find The Volume Of A Prism

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

All Intermediate Geometry Resources

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