Dilations
What is the variable used to represent scale factors?
k
How many faces are there on a cube?
6 faces
What is the volume of a cube whose side lengths are 1 meter each?
1 m3
"One cubic meter"
What is the word that describes the distance around a circle?
circumference
What is the word for a triangle with three equal side lengths?
equilateral triangle
When dilating a solid by a scale factor of k, all lengths are multiplied by k, all areas are multiplied by k2 and all volumes are multiplied by _____?
k3 ("k cubed")
24 ft2
6k2 = 6 * 22 = 6 * 4 = 24
What is the volume of a rectangular prism whose side dimensions are 4cm x 5cm x 5cm?
100 cm2
What is the word that describes half the length of the diameter of a circle?
radius
What is the formula for the area of a triangle?
(1/2)bh
220 cm2
55 * 22 = 55 * 4 = 220
The equation for the surface area of a sphere is 4πr2. In terms of π, what is the surface area of a sphere whose radius is 5 inches?
500π in2
The formula for the volume of a sphere is (4/3)πr3. In terms of π, what is the volume of a sphere whose radius is 3 inches?
36π in3
What is the formula for the area of a circle?
πr2
A right triangle has leg lengths of 6ft and 8ft. What is the length of the hypotenuse? (You must use the Pythagorean Theorem.)
10ft
A solid has a volume of 16 in3 and is dilated by a factor of k = 0.5. What is the volume of the dilated solid?
2 in3
16 * (1/2)3 = 16 * (1/8) = 2
What is the surface area of a rectangular prism whose dimensions are 3cm x 4cm x 5cm ?
94 cm2
To calculate the volume of a cylinder, multiply the area of the base times the height. In terms of pi, what is the volume of a cylinder whose bases have a radius of 7 cm, and whose height is 2 cm?
98 cm3
What is the formula for the circumference of a circle?
2πr
dπ
What is the area of an isosceles triangle whose base is 2 cm and whose other two side lengths are 6 cm? Round your answer to the nearest hundredth.
5.92cm2
A dilated solid has a volume of 270 m3. Before it was dilated, the solid had a volume of 10 m3. What was the scale factor?
k = 3
A cube has a volume of 64 ft3. What is its surface area?
96 ft2
The volume of a pyramid is given by the formula
length*width*height / 3
If a square pyramid has a height of 4.5 ft and a volume of 3.375 ft3, what are the dimensions of the base?
1.5 ft x 1.5 ft
What is the area of a circle inscribed in a square whose side lengths are one unit?
π/4 units2
What is the area of a circle whose diameter is 10 inches?
25π in2