Scale Drawing & Scale Factor
Is a scale factor of 1/2 a reduction or enlargement?
reduction
To form a triangle, the sum of the two smaller sides must be greater or smaller than the third side?
greater
What is the formula for finding the circumference of a circle?
c = pi x d
What is the sum of complementary angles?
90 degrees
What is the formula used to find the area of a triangle?
a = 1/2 x b x h
A flagpole uses a scale of 1 inch = 6 feet.
If the pole measures 12 inches, how tall is the actual pole?
72 ft
You are given two wooden sticks that are 7 inches and 11 inches long. What is the range of possible lengths (in inches) for a third stick that would allow you to form a triangle? Write your answer as an inequality.
4 < x < 18
radius
The angles in a diagram are complementary. One angle is (4x)° and the other is (2x + 6)°. What is the value of x?
x = 14
A rectangular pool cover is 30 feet long and 15 feet wide. If the material costs $0.50 per square foot, how much will the cover cost?
$225
On a map, Memphis, Tennessee, and Jackson, Mississippi, are 5 inches apart. The distance between the cities is actually 210 miles.
What scale was used to create the map?
1 in = 42 miles
If a triangle has two sides that measure 13 inches and 20 inches, what is the smallest possible whole-number length for the third side?
8 inches
Find the radius of a circle with a circumference of 28 centimeters.
4.45
Three angles are adjacent and their combined measure forms a right angle. The first angle is 25°, the second is 35°, and the third is x°. What is the value of x?
x = 30
The volume of a right rectangular prism is 120 cm3. If the length is 5 cm and the width is 4 cm, what is the height of the prism?
6 cm
A blueprint of a rectangular room uses a scale where 2 centimeters = 5 feet. If the room is 10 centimeters long on the blueprint, what is the actual length of the room?
25 ft
If the measures of two interior angles of a triangle are 48 degrees and 102 degrees, what is the measure of the third angle?
30 degrees
The wheel of a bicycle has a diameter of 24 inches. Approximately how far, in inches, will the bicycle travel after the wheel makes one complete rotation?
C = 3.14 × 24 = 75.36 inches
Angle 1 and Angle 2 are supplementary. Angle 1 measures (5x + 10)° and Angle 2 measures 70°. Find the value of x.
x = 20
A rectangular fish tank is 24 inches long and 12 inches wide. If the tank is filled with water to a height of 10 inches, what is the volume of the water in cubic inches?
v = 2880 cm3
A scale drawing of a rectangular garden has a scale of 1 inch = 4 feet. On the drawing, the garden is 5 inches long and 3 inches wide. What is the actual area of the garden in square feet?
240 sq ft
An isosceles triangle is drawn with one angle measuring 80° and the other two base angles measuring 50° each. Does this create a unique triangle, more than one triangle, or no triangle?
more than one triangle
A seventh-grade class is building a circular mini-golf green. If the circle is 10 feet in diameter, how many square feet of grass carpet will they need to buy to cover the entire circle? (Use 3.14 for pi)
Area = 3.14 × 52 = 78.5 sq ft
Two lines intersect to form four angles. One of the angles measures 125°. Its adjacent angle is represented by the expression (2x−5)°. What is the value of x?
x = 30
What is the surface area of a cube with a side length of 4 centimeters?
SA = 96 cm2