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Example Questions

Example Question #3 : Non Cubic Prisms

Find the surface area of the following triangular prism.

Triangular_prism

Possible Answers:

$216 + 216\sqrt{3}m^2$

$216 + 16\sqrt{3}m^2$

$218 + 16\sqrt{3}m^2$

$216 + 18\sqrt{3}m^2$

$18 + 18\sqrt{3}m^2$

Correct answer:

$216 + 18\sqrt{3}m^2$

Explanation:

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

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

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

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

Plugging in our values, we get:

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

$SA = 216 + 18\sqrt{3}m^2$

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

David wants to paint the walls in his bedroom. The floor is covered by a $10\ ft \times 16\ ft$ carpet. The ceiling is $8\ ft$ tall. He selects a paint that will cover $75\ ft^2$ per quart and $300\ ft^2$ per gallon. How much paint should he buy?

Possible Answers:

2 gallons and 1 quart

1 gallon

3 quarts

1 gallon and 2 quarts

1 gallon and 1 quart

Correct answer:

1 gallon and 2 quarts

Explanation:

Find the surface area of the walls: SA_walls = 2lh + 2wh, where the height is 8 ft, the width is 10 ft, and the length is 16 ft.

This gives a total surface area of 416 ft². One gallon covers 300 ft², and each quart covers 75 ft², so we need 1 gallon and 2 quarts of paint to cover the walls.

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

A box is 5 inches long, 5 inches wide, and 4 inches tall. What is the surface area of the box?

Possible Answers:

$25\ in^2$

$100\ in^2$

$130\ in^2$

$140\ in^2$

$120\ in^2$

Correct answer:

$130\ in^2$

Explanation:

The box will have six total faces: an identical "top and bottom," and identical "left and right," and an identical "front and back." The total surface area will be the sum of these faces.

Since the six faces consider of three sets of pairs, we can set up the equation as:

$SA=2(\text{top})+2(\text{left})+2(\text{front})$

Each of these faces will correspond to one pair of dimensions. Multiply the pair to get the area of the face.

SA=2(lw)+2(wh)+2(lh)

Substitute the values from the question to solve.

SA=2(5*5)+2(5*4)+2(5*4)

SA=50+40+40

$SA=130\ in^2$

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

What is the surface area of a rectangular brick with a length of 12 in, a width of 8 in, and a height of 6 in?

Possible Answers:

$576\ in^2$

$432\ in^2$

None of the answers are correct

$382\ in^2$

$216\ in^2$

Correct answer:

$432\ in^2$

Explanation:

The formula for the surface area of a rectangular prism is given by:

SA = 2LW + 2WH + 2HL

SA = 2(12 * 8) + 2(8 * 6) + 2(6 * 12)

SA = 2(96) + 2(48) + 2(72)

SA = 192 + 96 + 144

SA = 432 in²

216 in² is the wrong answer because it is off by a factor of 2

576 in³ is actually the volume, V = L * W * H

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Example Question #3 : Non Cubic Prisms

What is the surface area of an equilateral triangluar prism with edges of 6 in and a height of 12 in?

Let $\sqrt{3}=1.732$ and $\sqrt{2}=1.414$ .

Possible Answers:

$189.239\ in^{2}$

$268.732\ in^{2}$

$165.135\ in^{2}$

$247.176\ in^{2}$

$216.414\ in^{2}$

Correct answer:

$247.176\ in^{2}$

Explanation:

The surface area of the prism can be broken into three rectangular sides and two equilateral triangular bases.

The area of the sides is given by: $A=lw=12\cdot 6=72\ in^{2}$ , so for all three sides we get $\dpi{100} 216\ in^{2}$ .

The equilateral triangle is also an equiangular triangle by definition, so the base has congruent sides of 6 in and three angles of 60 degrees. We use a special right traingle to figure out the height of the triangle: 30 - 60 - 90. The height is the side opposite the 60 degree angle, so it becomes $3\sqrt{3}$ or 5.196.

The area for a triangle is given by $A=\frac{1}{2}bh$ and since we need two of them we get $A=bh=6\cdot 3\sqrt{3}=31.176\ in^{2}$ .

Therefore the total surface area is $216\ in^{2}+31.176\ in^{2}=247.176\ in^{2}$ .

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

Find the volume of the following triangular prism.

Half_box

Possible Answers:

182m^3

172m^3

152m^3

162m^3

142m^3

Correct answer:

162m^3

Explanation:

The formula for the volume of a triangular prism is:

$V = \frac{1}{2} (l)(w)(h)$

Where is the length of the triangle, is the width of the triangle, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2} (6m)(6m)(9m)$

V = 162m^3

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

Find the volume of the following triangular prism.

Half_box

Possible Answers:

384m^3

364m^3

394m^3

374m^3

404m^3

Correct answer:

384m^3

Explanation:

The formula for the volume of a triangular prism is:

V = (base)(height)

$V = \frac{1}{2}(l)(w)(h)$

Where is the length of the base, is the width of the base, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2}(8m)(8m)(12m)$

V = 384m^3

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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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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #3 : Non Cubic Prisms

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

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

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

Example Question #3 : Non Cubic Prisms

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

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

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

All High School Math Resources

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