Formulas
Pi times the radius squared is the formula to find the area of what shape?
Circle
If you draw a straight line through the entire circle, crossing through the center point, what is that line called?
diameter
What shape is the base of a cylinder?
a circle
A prism with a base of 4ft squared and a height of 6 feet has a volume of 24 cubic feet.
What's the volume of a pyramid with a base of 4 feet squared and a height of 6 feet?
8 cubic feet. You already know the volume of the prism with the same base and height is 24, so just take 1/3 of that and end up with 8.
Name an example of a real-life sphere.
a ball, an orange, Earth, etc.
1/3 base times height is the formula to find the volume of what shape?
A pyramid or a cone
A straight line from the center of a circle out to the edge is called the ______
radius
A prism has a square 2ft by 2ft base, and is 6 feet tall. What's the volume?
24 feet cubed
2 x 2 x 6 = 24
A cylinder has base area of 11 feet squared, and a height of 6 feet. The cylinder's volume is 66 cubic feet. What is the volume of a cone with the same base area and height?
22 cubic feet. A cone is 1/3 of a cylinder with the same base and height.
What is half a sphere called?
hemisphere
Base times height is the formula for to find the volume of what shape?
Cylinder or prism
If the diameter is 12, what is the radius?
6
A triangular prism's base has an area of 9 meters. The prism is 11 meters tall. What is the volume of the prism?
99 meters cubed
You already know the area of the base, so you just multiply that by the height. 9 x 11 = 99.
Which has more volume: a cone with a base of 8 square inches and a height of 6 inches, or a cylinder with a base of 8 square inches and a height of 5 inches?
The cylinder!
8 x 6 is 48, but then you have to divide it by 3. You'll end up with 16.
The cylinder you just multiply 8 times 5 and get 40.
What is a great circle?
The base of a hemisphere
4/3, times pi, times the radius cubed, is the formula to find the _____ of a ______
the volume of a sphere
If the diameter is 10 inches, what is the circumference? You must include the correct unit.
31.4 inches (circumference is diameter times pi)
You'd first have to multiply the radius by itself. You'd get 25.
You'd multiply 25 and 3.14 together to get the area of the base.
Then you'd multiply that number by 3 to get the volume.
Which of the following 4 shapes do you need pi to find the volume of: pyramid, cone, cylinder, prism
Cone and cylinder
pi times the radius cubed times what fraction equals the volume of a sphere?
4/3
4 times the area of the base of a _______ will get you the surface area of a ________
4 times the area of the base of a hemisphere will get you the surface area of a sphere.
If the diameter is 20 feet, what is the area? You must include the correct unit.
314 feet squared
(Area is radius times itself times pi. Radius is half of diameter, so the radius is 10. 10 times 10 is 100. 100 times 3.14 is 314.)
The base of a cylinder has a diameter of 16cm. The cylinder is 40 cm tall. How would you find the volume of the cylinder?
You'd first have to find the radius, which is half the diameter. Radius = 8.
8 squared is 64. You'd have to multiply 64 by pi (3.14) and then multiply that by 40 to get the volume.
How would you find the volume of an 8-foot tall cone in which the radius of the base is 3 square inches?
(you don't have to actually solve it)
First you'd find 3 squared, which is 9.
Then you'd multiply 9 by pi.
Then you'd multiply that answer by 8.
Then you'd divide by 3.
2-part question. Assuming all your measurements were done in centimeters...
1. What unit is the volume of a sphere written in?
2. What unit is the surface area of a sphere written in?
(you need to get them BOTH right in order for this to count)
1. centimeters cubed
2. centimeters squared