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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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

Find the surface area of the rectangular prism:

Volume_of_a_prism

Possible Answers:

$453\:units^3$

$468\:units^3$

$418\:units^3$

$410\:units^2$

$468\:units^2$

Correct answer:

$410\:units^2$

Explanation:

The surface area of a rectangular prism is

SA=2lw+2lh+2wh

Substituting in the given information for this particular rectangular prism.

$\\SA=2(13\cdot 9)+2(13\cdot 4)+2(9\cdot 4) \\SA=410\ \text{units}^2$

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Example Question #3 : How To Find The Volume Of A Prism

A small rectangular fish tank has sides that are 18in wide, 30in long, and 24in high. Which formula would not work to find the correct volume of the fish tank?

Possible Answers:

$720 \times 18$

$(18 \times 30) + 24$

$(30 \times 24) \times 18$

$30 \times 432$

$(24 \times 18) \times 30$

Correct answer:

$(18 \times 30) + 24$

Explanation:

In this question the formula that uses addition will not yield the correct volume of the fish tank:

(18 x 30) + 24

This is the correct answer because in order to find the volume of any rectangular prism one needs to multiply the prism's length, width, and height together.

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$

In this equation, is length, is width, and is height.

To restate, (18 x 30) + 24 is the correct answer because it will NOT yield the correct volume, you would need to multiply by the product of and , not add.

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Example Question #21 : Prisms

Find the volume of the prism.

Possible Answers:

1800

1960

1720

1880

Correct answer:

1800

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(12)(15)=90$

Now, find the volume of the prism.

$\text{Volume of Prism}=90 \times 20 =1800$

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

Find the volume of the prism.

Possible Answers:

450

360

270

540

Correct answer:

270

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(3)(9)=13.5$

Now, find the volume of the prism.

$\text{Volume of Prism}=13.5\times 20 =270$

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Example Question #161 : Solid Geometry

Find the volume of the prism.

Possible Answers:

335

305

325

315

Correct answer:

315

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(5)(9)=22.5$

Now, find the volume of the prism.

$\text{Volume of Prism}=22.5\times 14=315$

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Example Question #8 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

696

690

684

678

Correct answer:

684

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(6)(12)=36$

Now, find the volume of the prism.

$\text{Volume of Prism}=36\times 19=684$

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Example Question #9 : How To Find The Volume Of A Prism

Find the volume of a prism.

Possible Answers:

450

580

690

510

Correct answer:

510

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(5)(12)=30$

Now, find the volume of the prism.

$\text{Volume of Prism}=30\times 17=510$

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Example Question #31 : Prisms

Find the volume of the prism.

Possible Answers:

2070

2050

2090

2210

Correct answer:

2210

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(13)(17)=110.5$

Now, find the volume of the prism.

$\text{Volume of Prism}=110.5\times 20 =2210$

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Example Question #32 : Prisms

Find the volume of the prism.

Possible Answers:

3768

3458

3558

3658

Correct answer:

3458

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(13)(19)=123.5$

Now, find the volume of the prism.

$\text{Volume of Prism}=123.5\times 28 =3458$

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Example Question #11 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(1)(4)=2$

Now, find the volume of the prism.

$\text{Volume of Prism}=2\times 4=8$

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

Example Question #3 : How To Find The Volume Of A Prism

Example Question #21 : Prisms

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

Example Question #161 : Solid Geometry

Example Question #8 : How To Find The Volume Of A Prism

Example Question #9 : How To Find The Volume Of A Prism

Example Question #31 : Prisms

Example Question #32 : Prisms

Example Question #11 : How To Find The Volume Of A Prism

All Intermediate Geometry Resources

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