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Common Core: 7th Grade Math : Solve for surface area

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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Example Questions

Example Question #71 : Geometry

The length of the side of a cube is x -5 $\displaystyle x -5$. Give its surface area in terms of $\displaystyle x$.

Possible Answers:

$6x^{2} -60x - 150$ $\displaystyle 6x^{2} -60x - 150$

$6x^{2} -10x + 25$ $\displaystyle 6x^{2} -10x + 25$

$\displaystyle x^3-15 x^2-75 x+125$

$6x^{2} -60x + 150$ $\displaystyle 6x^{2} -60x + 150$

$\displaystyle x^3-15 x^2+75 x-125$

Correct answer:

$6x^{2} -60x + 150$ $\displaystyle 6x^{2} -60x + 150$

Explanation:

Substitute $\displaystyle s = x - 5$ in the formula for the surface area of a cube:

$A = 6s^{2}$ $\displaystyle A = 6s^{2}$

$A = 6 \left ( x - 5\right )^{2}$ $\displaystyle A = 6 \left ( x - 5\right )^{2}$

$A = 6 \left ( x^{2} - 2 \cdot 5 \cdot x + 5^{2}\right )$ $\displaystyle A = 6 \left ( x^{2} - 2 \cdot 5 \cdot x + 5^{2}\right )$

$A = 6 \left ( x^{2} - 10x +25\right )$ $\displaystyle A = 6 \left ( x^{2} - 10x +25\right )$

$A = 6 x^{2} - 60x +150$ $\displaystyle A = 6 x^{2} - 60x +150$

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Example Question #901 : Grade 7

If a cube has one side measuring $\displaystyle 4$ cm, what is the surface area of the cube?

Possible Answers:

$\displaystyle 96$

$\displaystyle 26$

$\displaystyle 24$

$\displaystyle 16$

$\displaystyle 22$

Correct answer:

$\displaystyle 96$

Explanation:

To find the surface area of a cube, use the formula $6s^{2}$ $\displaystyle 6s^{2}$, where $\displaystyle s$ represents the length of the side. Since the side of the cube measures $\displaystyle 4$, we can substitute $\displaystyle 4$ in for $\displaystyle s$.

$6(4)^{2}=96\: cm^{2}$ $\displaystyle 6(4)^{2}=96\: cm^{2}$

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Example Question #1 : Solve For Surface Area

Find the surface area of a non-cubic prism with the following measurements:

$\displaystyle l=7;w=6;h=2$

Possible Answers:

136 $\displaystyle 136$

$\displaystyle 84$

$\displaystyle 68$

168 $\displaystyle 168$

Correct answer:

136 $\displaystyle 136$

Explanation:

The surface area of a non-cubic prism can be determined using the equation:

$\displaystyle SA=2lw+2wh+2lh$

$\displaystyle SA=2(7)(6)+2(6)(2)+2(7)(2)=84+24+28=136$

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Example Question #1101 : Intermediate Geometry

A small rectangular jewelry box has two square ends with areas of 36 square centimeters, and a width of 10 centimeters. What is the surface area of the outside of the jewelry box.

Possible Answers:

$360 \; cm^2$ $\displaystyle 360 \; cm^2$

$216 \; cm^2$ $\displaystyle 216 \; cm^2$

$72 \; cm^2$ $\displaystyle 72 \; cm^2$

$312 \; cm^2$ $\displaystyle 312 \; cm^2$

$240 \; cm^2$ $\displaystyle 240 \; cm^2$

Correct answer:

$312 \; cm^2$ $\displaystyle 312 \; cm^2$

Explanation:

To find the surface area of the rectangular box we just need to add up the areas of all six sides. We know that two of the sides are 36 square centimeters, that means we need to find the areas of the four mising sides. To find the area of the missing sides we can just multiply the side of one of the squares (6 cm) by the width of the box:

$6 \times 10 = 60 \; cm^2$ $\displaystyle 6 \times 10 = 60 \; cm^2$

But remember we have four of these rectangular sides:

$4 \times 60 = 240 \; cm^2$ $\displaystyle 4 \times 60 = 240 \; cm^2$

Now we just add the two square sides and four rectangular sides to find the total surface area of the jewelry box:

$36 \; cm^2 + 36 \; cm^2 + 240 \; cm^2 = 312 \; cm^2$ $\displaystyle 36 \; cm^2 + 36 \; cm^2 + 240 \; cm^2 = 312 \; cm^2$

That is the total surface area!

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Example Question #72 : Geometry

Alice is wrapping a rectangular box that measures $5\textup {in}\times 6\textup {in}\times 12\textup {in}$ $\displaystyle 5\textup {in}\times 6\textup {in}\times 12\textup {in}$. How many square feet of wrapping paper does she need?

Possible Answers:

$2.75 \textup{ ft}^{2}$ $\displaystyle 2.75 \textup{ ft}^{2}$

$2.00 \textup{ ft}^{2}$ $\displaystyle 2.00 \textup{ ft}^{2}$

$2.25\textup{ ft}^2$ $\displaystyle 2.25\textup{ ft}^2$

$1.75\textup{ ft}^{2}$ $\displaystyle 1.75\textup{ ft}^{2}$

$3.25\textup{ ft}^{2}$ $\displaystyle 3.25\textup{ ft}^{2}$

Correct answer:

$2.25\textup{ ft}^2$ $\displaystyle 2.25\textup{ ft}^2$

Explanation:

The surface area of a rectangular prism is given by

$\textup {SA=2lw+2lh+2wh}$ $\displaystyle \textup {SA=2lw+2lh+2wh}$ where $\displaystyle l$ is the length, $\displaystyle w$ is the width, and $\displaystyle h$ is the height.

Let $\textup l=5\textup { in}$ $\displaystyle \textup l=5\textup { in}$, $\textup {w}=6\textup{ in}$ $\displaystyle \textup {w}=6\textup{ in}$, and $\textup {h}=12\textup { in}$ $\displaystyle \textup {h}=12\textup { in}$

So the equation to solve becomes $\textup SA=2\cdot 5\cdot 6+2\cdot 5\cdot 12+2\cdot 6\cdot 12$ $\displaystyle \textup SA=2\cdot 5\cdot 6+2\cdot 5\cdot 12+2\cdot 6\cdot 12$ or $324\textup{ in}^{2}$ $\displaystyle 324\textup{ in}^{2}$

However the question asks for an answer in square feet. Knowing that $144\textup { in}^{2}=1\textup { ft}^{2}$ $\displaystyle 144\textup { in}^{2}=1\textup { ft}^{2}$ we can convert square inches to square feet. It will take $2.25\textup{ ft}^{2}$ $\displaystyle 2.25\textup{ ft}^{2}$ of paper to wrap the present.

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Common Core: 7th Grade Math : Solve for surface area

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #71 : Geometry

Example Question #901 : Grade 7

Example Question #1 : Solve For Surface Area

Example Question #1101 : Intermediate Geometry

Example Question #72 : Geometry

All Common Core: 7th Grade Math Resources

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