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Unit 7 –Volume 13 Volume of rectangular solids 12 Volume of cylinders 11 Volume of cones 10 Volume...

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Unit 7 –Volume 13 Volume of rectangular solids 12 Volume of cylinders 11 Volume of cones 10 Volume of pyramids 9 Volume of spheres 8 WP: Volume
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Unit 7 –Volume13 Volume of rectangular solids12 Volume of cylinders11 Volume of cones 10 Volume of pyramids9 Volume of spheres8 WP: Volume

13 Riddle

It's more powerful than God.It's more evil than the devil.The poor have it.The rich need it.If you eat it, you'll die.What is it?

13 RiddleWalks in the wind,Runs in the rain,

Makes dry oceans in the sun.Counts time, stops clocks,

Swallows kingdoms, gnaws rocks.

What is it?

13 Volume of rectangular prismsVolume for a prism

V=B•h

Ex1. Calculate the volume of a rectangular prism with dimensions 17ft by 5 ft by 3 ft.

17•5•3 = 255 ft3

“B” is the area of the base “h” is the object height (not the slant height)

5

3

9m4m

5m

Find the volume

17

V=Bh

B=10

V=10•9 = 90m3

12 Riddle

How can you plant ten trees in five rows with four trees in each row….?

12a Volume of cylinders

Volume = Area of Base • height

Volume of cylinder = r2•h

8cm

6cm

V=32•8

V=72 cm3

12b Volume of cylinders

Ex2. Find the volume. Use 22/7 for pi

Volume of cylinder = • r2 • h

14cm

10cm

11 Volume of cones

Two trains are headed on a collision course. The trains are currently 65 miles apart. The north bound train is traveling at 55 miles per hour and the south bound

train is traveling at 80 miles per hour. What is the distance between the two

trains just before they collide?

11a Volume of cones

Any “pyramid” type of shape has 1/3 the volume of the prism.

3

hBV

h is the object height (not slant height)

B is the area of the Base

Volume of a cone 3

2hrV

11b Volume of cones

12m

Find the exact volume.

3

2hrV

3

1282V

3

768V

V = 256 m3

8m

A couple went for a walk as they were holding hands. However, one walked further than the other, how is this possible?

10 Volume of pyramids

10a Volume of pyramids

Any “pyramid” type of shape has 1/3 the volume of the prism.

3

hBV

B is the area of the Base

h is the object height (not slant height)

Find the volume:

3

172018 V

3

6120V 32040m

9 Volume of spheres

I have three USA coins. They are not a quarter, nor a dime, or a penny. It adds up to 60 cents. What are the coins?

9a Volume of spheresSurface area of a sphere

A=4r2 units2

Volume of a sphere

33

3

4units

rV

Find the volume of a sphere with a diameter of 8mm

3

4 3rV

3

44 3V

3

644V 3

3

256mm

268.1 mm3

8 WP: Volume

What is the sum of the numbers from 1 to 100?

8a WP: Volume

Ex1. A fish tank is 26 inches tall and has a base that is 15 inches by 22 inches. You want to fill the tank to a depth of 24 inches. How much water will it take?

8b WP: VolumeEx2. Ricardo is wrapping a gift to take to a birthday party and needs a box to put the gift in. The only box he has measures 4 in. 6 in. 6 in. He needs a box with measurements 3 times as large. What is the volume of the box Ricardo needs? How does the volume compare to that of the box he already has?

8c WP: Volume

Ex3. A cylindrical oil storage tank has a height of 16 m and a diameter of 12 m. If the tank is 50full, how many kiloliters of oil, to the nearest tenth, does it contain? Use 3.14. (1 kL = 1 m3)

8d WP: VolumeThe inside of an ice cream cone has radius 5 cm and height 9 cm. Assuming that a half-scoop of ice cream is in the shape of a hemisphere, (half a sphere) and that it fits perfectly on top of the cone (same radius), find the total volume of ice cream cone. Round to the nearest tenth.

5

9

Volume of Sphere Volume of cone

Volume = r2h/3

l3

4 3rV


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