Geometry

7th Grade Math · Learn by Concept

Help Questions

7th Grade Math › Geometry

1 - 10

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

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

CORRECT

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

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

Explanation

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

$A = 6s^{2}$

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

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

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

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

Box

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

CORRECT

$15x^{2}$

$4x^{2} + 30 x$

Explanation

A square has four sides of equal length, as seen in the diagram below.

Box

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

What angle is complement to $\frac{\pi}{6}$ ?

$\frac{\pi}{3}$

CORRECT

$\frac{\pi}{9}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{2\pi}{3}$

Explanation

The complement to an angle is ninety degrees subtract the angle since two angles must add up to 90. In this case, since we are given the angle in radians, we are subtracting from $\frac{\pi}{2}$ instead to find the complement. The conversion between radians and degrees is: $\pi \textup{ radians } = 180 \textup{ degrees}$

$\frac{\pi}{2}-\frac{\pi}{6}$

Reconvert the fractions to the least common denominator.

$\frac{\pi}{2}-\frac{\pi}{6} = \frac{3\pi}{6}-\frac{\pi}{6} = \frac{2\pi}{6}$

Reduce the fraction.

$\frac{2\pi}{6} = \frac{\pi}{3}$

6 8 10

What is the area of the triangle pictured above?

CORRECT

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.

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

CORRECT

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

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

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

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

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:

$V=11\times11\times11$

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

Calculate the area of the provided figure.

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

CORRECT

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

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

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

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

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 volume of the provided figure.

$240\textup{ in}^3$

CORRECT

$241\textup{ in}^3$

$242\textup{ in}^3$

$243\textup{ in}^3$

$244\textup{ in}^3$

Explanation

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

$V=l\times w\times h$

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

$V=10\times4\times6$

$V=240\textup{ in}^3$

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

CORRECT

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 .

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

Abcd

In triangle ABC above, the distance between point A and point D is 10 inches, and the area of the triangle is 20 square inches. What is the length of side BC?

4 inches

CORRECT

2 inches

10 inches

8 inches

There is not enough information to answer the question