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ACT Math : Prisms

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Example Question #1 : 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:

$216\ in^2$

$382\ in^2$

None of the answers are correct

$576\ in^2$

$432\ in^2$

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 #1 : How To Find The Volume Of A Prism

A box's length is twice as long as its width. Its height is the sum of its length and its width. What is the volume of this box if its length is 10 units?

Possible Answers:

250 units cubed

750 units cubed

150 units cubed

500 units cubed

300 units cubed

Correct answer:

750 units cubed

Explanation:

The formula for the volume of a rectangular prism is V = L*W*H , where "" is volume, "" is length, "" is width and "" is height.

We know that L = 2W and H = L+W . By rearranging L=2W , we get $W=\frac{L}{2}$ . Substituting $\frac{L}{2}$ into the volume equation for and L+W into the same equation for , we get the following:

$V = L \cdot \left(\frac{L}{2}\right)\cdot (L+\left(\frac{L}{2}\right))$

$V = L\cdot \left(\frac{L}{2}\right)\cdot \frac{3L}{2}$

$V = 10 \cdot 5 \cdot 15$

V = 750 units cubed

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Example Question #3 : Finding Volume Of A Rectangular Prism

A rectangular prism has the following dimensions:

Length: $6.3 \:cm$

Width: $6.3 \:cm$

Height: $2.1 \:cm$

Find the volume.

Possible Answers:

$84.9\:cm^3$

$83.3\:cm^3$

$83.4\:cm^3$

$83.8\:cm^3$

$84.3\:cm^3$

Correct answer:

$83.3\:cm^3$

Explanation:

Given that the dimensions are: $6.3 \:cm$ , $6.3 \:cm$ , and $2.1 \:cm$ and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

V = (6.3)(6.3)(2.1)

V = (39.69)(2.1)

$V = 83.349\:cm^3$

This final value can be approximated to $83.3\:cm^3$ .

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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 #91 : Geometry

Solve for the volume of a prism that is 4m by 3m by 8m.

Possible Answers:

V=88m^3

V = 136 m^3

V = 102 m^3

V = 144 m^3

V = 96 m^3

Correct answer:

V = 96 m^3

Explanation:

The volume of the rectangle

V = l*w*h

so we plug in our values and obtain

V = 4*3*8

V = 96 m^3 .

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ACT Math : Prisms

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

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

Example Question #3 : Finding Volume Of A Rectangular Prism

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

Example Question #91 : Geometry

All ACT Math Resources

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