Solve Problems Involving Area, Volume and Surface Area of Two- and Three-Dimensional Objects: CCSS.Math.Content.7.G.B.6

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7th Grade Math › Solve Problems Involving Area, Volume and Surface Area of Two- and Three-Dimensional Objects: CCSS.Math.Content.7.G.B.6

Questions 1 - 10

The length of the side of a cube is . Give its surface area in terms of .

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

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

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

Explanation

Substitute in the formula for the surface area of a cube:

$A = 6s^{2}$

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

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

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

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

6 8 10

What is the area of the triangle pictured above?

Explanation

The area of a triangle is calculated using the formula $Area = \frac{1}{2}(Base\times Height)$ . Importantly, the height is a perpendicular line between the base and the opposite point. In a right triangle like this one, you're in luck: the triangle as drawn already has that perpendicular line as one of the two sides. So here we will calculate $\frac{1}{2}(8\times 6)$ . That gives us an answer of 24.

Calculate the volume of the provided figure.

$1\textup,331\textup{ in}^3$

$1\textup,332\textup{ in}^3$

$1\textup,333\textup{ in}^3$

$1\textup,334\textup{ in}^3$

$1\textup,335\textup{ in}^3$

Explanation

In order to solve this problem, we need to recall the volume formula for a cube:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=11\times11\times11$

$V=1\textup,331\textup{ in}^3$

The length of the side of a cube is . Give its surface area in terms of .

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

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

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

Explanation

Substitute in the formula for the surface area of a cube:

$A = 6s^{2}$

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

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

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

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

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

Explanation

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

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

Calculate the area of the provided figure.

$361\pi\textup{ in}^2$

$360\pi\textup{ in}^2$

$362\pi\textup{ in}^2$

$363\pi\textup{ in}^2$

$364\pi\textup{ in}^2$

Explanation

In order to solve this problem, we need to recall the area formula for a circle:

$A=r^2\pi$

Now that we have the correct formula, we can substitute in our known values and solve:

$A=19^2\pi$

$A=361\pi\textup{ in}^2$

Calculate the area of the provided figure.

$361\pi\textup{ in}^2$

$360\pi\textup{ in}^2$

$362\pi\textup{ in}^2$

$363\pi\textup{ in}^2$

$364\pi\textup{ in}^2$

Explanation

In order to solve this problem, we need to recall the area formula for a circle:

$A=r^2\pi$

Now that we have the correct formula, we can substitute in our known values and solve:

$A=19^2\pi$

$A=361\pi\textup{ in}^2$

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

Explanation

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

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

Calculate the volume of the provided figure.