Geometry

Help Questions

Math › Geometry

Questions 1 - 10

Find the area of the following sector:

$9 \pi\ m^2$

$18 \pi\ m^2$

$6 \pi\ m^2$

$3 \pi\ m^2$

$12 \pi\ m^2$

Explanation

The formula for the area of a sector is

$A = \pi r^2 (part)$ ,

where is the radius of the circle and is the fraction of the sector.

Plugging in our values, we get:

$A = \pi (6\ m)^2 (\frac{90}{360})$

$A=9 \pi\ m^2$

Which is the greater quantity?

(a) The sidelength of a square with area square inches.

(b) The sidelength of a square with perimeter inches.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell which is greater from the information given.

Explanation

The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:

(a) A square with area square inches has sidelength $\sqrt{225} = 15$ inches.

(b) A square with perimeter inches has sidelength $50 \div 4 = 12.5$ inches.

(a) is the greater quantity.

To the nearest tenth, give the area of a circle with diameter 17 inches.

$227.0 \textrm{ in}^{2}$

$907.9\textrm{ in}^{2}$

$289.0 \textrm{ in}^{2}$

$454.0\textrm{ in}^{2}$

$578.0\textrm{ in}^{2}$

Explanation

The radius of a circle with diameter 17 inches is half that, or 8.5 inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 8.5^{2} \approx 227.0$

To the nearest tenth, give the area of a $60^{\circ }$ sector of a circle with diameter 18 centimeters.

$42.4 \textrm{ cm}^{2}$

$84.8 \textrm{ cm}^{2}$

$169.6 \textrm{ cm}^{2}$

$21.2 \textrm{ cm}^{2}$

$254.5 \textrm{ cm}^{2}$

Explanation

The radius of a circle with diameter 18 centimeters is half that, or 9 centimeters. The area of a $60^{\circ }$ sector of the circle is

$A = \frac{60}{360 }\cdot \pi \cdot 9^{2} =\frac{1}{6} \cdot \pi \cdot 81 \approx 42.4 \textrm{ cm}^{2}$

What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?

100

100√2

50√2

200√2

Explanation

Square_part1

Square_part2

Square_part3

is a positive number. Which is the greater quantity?

(A) The volume of a cube with edges of length

(B) The volume of a sphere with radius

(A) is greater

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

Explanation

No calculation is really needed here, as a sphere with radius - and, subsequently, diameter - can be inscribed inside a cube of sidelength . This makes (A), the volume of the cube, the greater.

A pentagon with a perimeter of one mile has three congruent sides. The second-longest side is 250 feet longer than any one of those three congruent sides, and the longest side is 500 feet longer than the second-longest side.

Which is the greater quantity?

(a) The length of the longest side of the pentagon

(b) Twice the length of one of the three shortest sides of the pentagon

(b) is greater.

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Explanation

If each of the five congruent sides has measure , then the other two sides have measures and $\left (x + 250 \right ) +500 = x + 750$ . Add the sides to get the perimeter, which is equal to feet, the solve for :

$5x\div 5 = 4,280 \div 5$

feet

Now we can compare (a) and (b).

(a) The longest side has measure feet.

(b) The three shortest sides each have length 856 feet; twice this is $856 \times 2 = 1,712$ feet.

(b) is greater.

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

Explanation

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

To find the area of a rectangle, we must perform the following:

$A_{Rectangle}=l*w$

Where l and w are our length and width.

This means we need to multiply the given measurements. Be sure to use the right units!

And we have our answer. It must be centimeters squared, because we are dealing with area.

Rectangle 1

The above rectangle, which has perimeter 360, is divided into squares of equal size. Give the area of the shaded portion.

Explanation

The sides of the rectangle, in total, are divided into 18 segments of equal measure, as indicated below:

Rectangle 2

The rectangle has a total perimeter of 360, so each segment - one side of a square - measures $36 0 \div 18 = 20$ . Each square has area $20 ^{2} = 400$ , so the shaded portion of the rectangle, which comprises seven squares, has area