Calculate the volume #4

Answer Key

1.05m

55cm

55 cm

It’s a Box!

V= L x W x T

V = L x W x T

= 1.05m x 55cm x 55cm

Whoops, won’t work – the units don’t match. A little King Henry and change it to

= 105cm x 55cm x 55cm

Ballpark 100 x 50 x 50 = 250 000

= 317 625 cm3

28.8 cm

35.2cm

18cmIt’s a Box!

V= L x W x T

V = L x W x T

= 35.2cm x 28.8cm x 18cm

Ballpark 30 x 30 x 20 = 18 000

= 18 247.68 cm3

52mm

4.2cm

20.2cm

It’s a Box!

V= L x W x T

V = L x W x T

= 20.2cm x 52mm x 4.2cm

Whoops, won’t work – the units don’t match. A little King Henry and change it to

= 20.2cm x 5.2cm x 4.2cm

Ballpark 20 x 5 x 4 = 400

= 441.17 cm3

30cm

38 cm

5cm

It’s a Triangle (a box cut diagonally in halfSoooo…

V= L x W x T /2

V = L x W x T /2

= 38cm x 30cm x 5cm

Ballpark 40 x30 x 5 = 6000

= 5 700 cm3

8dm diameter

It’s a Sphere!

V= 4/3 π r3

V= 4/3 π r3

= 4/3 x 3.14 4dm x 4dm x 4dm (r3 = r x r x r)

Ballpark 4/3 x 3 x 4 x 4 x 4 = 256

= 267.94 dm3 (look at that unit!)

Remember that the radius is half the diameter.

20cm

75mm

It’s a Cylinder

V= π r2h

V= π r2h

= 3.14 x 75mm x 75mm x 20cm

Whoops, won’t work – the units don’t match. A little King Henry and change it to

= 3.14 x 75mm x 75mm x 200mm OR

= 3.14 x 7.5cm x 7.5cm x 20cm

It doesn’t matter which way, one will give an answer in mm3 and one will give cm3

Ballpark 3 x 7 x 7 x 20 = 2940

= 3532.5 cm3

15 m

55 m

It’s a Cylinder

V= π r2h

V= π r2h

= 3.14 x 27.5m x 27.5m x 15m

Ballpark = 3 x 30 x 30 x 10 = 27 000

= 35 619.375 m3

19.5cm

6.5 cm

It’s a Cylinder

V= π r2h

V= π r2h

= 3.14 x 3.25cm x 3.25cm x 19.5cm

Ballpark = 3 x 3 x 3 x 20 = 540

= 646.74cm3

980 mm

9cm

It’s a Cylinder

V= π r2h

V= π r2h

= 3.14 x 4.5cm x 4.5cm x 980mm

Whoops, won’t work – the units don’t match. A little King Henry and change it to

= 3.14 x 4.5cm x 4.5cm x 98.0cm

Ballpark 3 x 5 x 5 x 100 =7500

= 6231.22 cm3

Dia = 2.5mm It’s a Sphere!

V= 4/3 π r3

V= 4/3 π r3

= 4/3 x 3.14 1.25mm x 1.25mm x 1.25mm (r3 = r x r x r)

Ballpark 4/3 x 3 x 1 x 1 x 1 = 4

= 8.18 mm3 (look at that unit!)

25.2 cm dia

35.5cm

19.5cm

It’s a Sphere on top of a cone!

V= 4/3 π r3 for the sphere

and V=1/3 π r2 h for the cone

There’s one more page!

Sphere V= 4/3 π r3

= 4/3 x 3.14 x 12.6cm x 12.6cm x 12.6cm

Ballpark 4/3 x 3 x 10 x 10 x 10 = 4000

= 8374.9 cm3

Cone V=1/3 π r2 h

= 1/3 x 3.14 x 9.75cm x 9.75cm x 35.5cm

Ballpark 1/3 x 3 x 10 x 10 x 30 = 3000

= 3532.2 cm3

Now add together the Sphere and the cone!

8374.9 cm3 + 3532.2 cm3

= 11 907.1cm3

Consider this a secret extra page – don’t tell anyone about it!!!! If you print out JUST THIS PAGE and solve the problem, I will give you extra credit for your effort!

I found this cool box and I want to fill it with M&M’s to send to my brother. What would be the total volume of this box?

You might find it helpful to sketch the box on the back of the paper to make it easier to break it into parts - try drawing it as if you were looking at the end of the box.

30cm20cm

15cm

25cm25cm

Name: ____________________ Science Pd _______

EXTRA EXTRA CREDIT If an M&M takes up about .8cm3 of space, roughly how many would fit in the box?