Surface Area & Volume
This 3D shape's volume is calculated using the formula V=l×w×h
rectangular prism
What three measurements do you need to find the volume of a rectangular prism?
length, width and height
A can of soup has a radius of 4 cm and a height of 10 cm. What is its volume?
502.7 cm3
True or False: The volume of a rectangular prism changes if you rotate it.
False
I am an odd number.
Take away one letter, and I become even.
seven
You can find the surface area of this shape by adding the area of its circular base and the curved side, using the formula SA=πr2+πrl
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
30 cm3
You're designing a new large smoothie cup for your café. The cup has a radius of 4 cm and a height of 10 cm.
How much smoothie does it hold in mL
1cm3= 1mL
500mL
You have two containers: one is a rectangular prism with dimensions 10 cm × 5 cm × 8 cm, and the other is a cylinder with a radius of 4 cm and a height of 8 cm. Which container holds more?
The cylinder
There are 3 birds on a tree. Two fly away.
How many legs are left on the tree?
Two legs
This formula gives the surface area of a cylinder:
SA=2πr2+2πrh
area of the base. area of lateral face(side)
r= radius
h= height
A rectangular box has a volume of 240 cm³ and a base area of 30 cm². What is its height?
8cm
You’re making handmade cylindrical candles. One candle mold has a diameter of 6 cm and a height of 10 cm.
How much wax will two candles require?
Round to the nearest hundredth.
565.48 cm3
If you double all the dimensions of a rectangular prism, how does its volume change?
How many times greater is the new volume?
When you double all the dimensions of a rectangular prism, the volume increases by a factor of 8.
So the new volume is 8 times greater than the original.
The Bat-Signal shines every 15 minutes. If it lights up at 7:00 PM, at what times will it shine before 8:00 PM?
Every 15 minutes means at 7:00, 7:15, 7:30, and 7:45 PM.
You're wrapping a gift shaped like a rectangular box and need to know how much paper is required. Are you finding surface area or volume?
surface area
The volume of a rectangular prism is 120 cm³. If the length is 6 cm and the width is 4 cm, what is the height?
5cm
A cylindrical tank has a diameter of 10 meters and a height of 6 meters. What is its volume?
471.2 m3
What is the difference between capacity and volume?
Volume is the amount of space an object occupies, while capacity is the amount of substance (like liquid or gas) that object can hold.
The Flash runs at 60 miles per hour. How far does he run in 45 minutes?
45 minutes = ¾ hour
Distance = speed × time = 60 × 0.75 = 45 miles
You're filling a cylindrical tank with water and need to know how much it can hold. Are you finding surface area or volume?
volume
A rectangular prism has a square base with side lengths of 7 cm and a height of 10 cm. What is its volume?
490 cm3
At a carnival, you buy a giant soda in a cylindrical cup with a diameter of 10 cm and a height of 30 cm.
How many milliliters of soda are in your cup?
1cm3 = 1 mL
2356.19 mL
You need to cover your bedroom floor with carpet. Which measurement do you need: area or volume?
area
Superman has 20 pieces of kryptonite. He gives half to Batman and a quarter to Wonder Woman. How many pieces does he keep?
Half to Batman = 20 × ½ = 10
Quarter to Wonder Woman = 20 × ¼ = 5
Total given = 10 + 5 = 15
Pieces left = 20 - 15 = 5 pieces