## Thursday, February 17, 2011

### Sandra's Volume Post

11. Copy and complete the chart:

Length Width Height Volume

a)7cm 2cm 5cm 70cm3

l

b)12cm 9cm 10cm 1080cm3

c)16cm 15cm 5cm 1200cm3

You can easily fill in this chart by simply asking yourself what multiplied by what equals the volume or creating an algebraic equation for each one. For example: a) 7x2=14, so 14xa=70m3, you replace the variable (a) with the number that best suits that equation which is 5. So thats how I figured out question 11.

16. Cindy’s aquarium stands 75 cm tall and
has a base that measures 1.2 m × 80 cm.
At one point during the initial fi lling, the
aquarium has a 12-cm depth of water in
it. Cindy needs to fi ll it to 15 cm from the
top
before she adds the fi sh. Draw a
diagram
and label the dimensions of the
aquarium. Determine how much more
water Cindy must add before she puts in
the fi sh.

Red=Math information

Scince you need a 15cm gap from the top you need to subtract 12 from 75 which is 63 and then you subtract 15 from 63 and you get 48. Now we have to find the volume of water we need to use in the tank.

V=lxwxh

v=120cmx80cmxh

v=9600cm2x48cm

v=460 800 cm3.

So Cindy needs to add 460 800cm3 of water before she adds the fish.

17.
A contractor is excavating a rectangular
hole 10 m × 12 m × 3 m to pour the
foundation for a house. A dump truck
with a capacity of 9 m3 is used to haul
away the excavated soil. How many trips
does the truck need to make?

Find volume of rectangular hole:

V=lxwxh

v=10mx12mxh

v=120m2x3m

v=360m3

360m3/9m3=40m3

So the truck driver will have to make 40 trips.

Cylinder Volume and Volume Problems

Cylinder Problem

Jumbo

d=r/2

d=20cm/2

d=10cm

v=πr^2 h

v=(3.14 10cm^2) 40cm

v=314cm^2 40cm

v=12560cm^3

Popcorn Lovers

r=d/2

r=30cm/2

r=15cm
v=πr^2 h

v=(3.14 15cm ^2) 20cm

v=706.5cm^2 20cm

v=14130cm^2

If Martha wants more popcorn for her money, she should get the popcorn lovers because it has a greater volume, that being said, you can fit more popcorn into it.

Volume Problem
A concrete culvert that is 10 cm long has an inside diameter of 0.8m and an outside diameter of 1m. Determine the volume of concrete required to make the culvert to the nearest tenth of a cubic centimetre.

Outside Diameter
r=d/2
r=1/2
r=0.5m
v=πr^2 h
v=(3.14 0.5^2) 10m

v=0.785cm^2 10m

v=7.85m^3

Inside Diameter

r= d/2
r=0.8/2
r=0.4m

V=πr^2 h

V=(3.14 0.4^2)h

V=0.5024m^3

To find the volume subtract the inside diameter from the outside diameter.

7.85m^3-o.5024m^3=7.3476m^3

Now we have to convert meters into centimetres.

We can do that by multiplying 7.3476 by 100, and that equals 734.76cm^3.

So you need 734.76cm^3 of concrete to make the culvert.