# Volume and area

• Apr 23rd 2009, 03:43 PM
Jubbly
Volume and area
Well I'm having troubles doing a few word problems about area and volume.
If you can show me how you do these much appreciated!

A coffee store sold two different cans.Regular and large. Dimensions of the large can is twice the dimension of the regular can. If the regular can has a volume of 72 cubic inches, what is the volume of the large can?

A sphere has a surfeace area of 6 square yards. The sphere is en;arged by a scale factor of 3 to produce a new sphere. what is the new surface area of the new sphere?
For this the answer I got was 18 square yards.

The Cylinders are similar. The Volume of the large cylinder is 64 cubic centimeters and the volume of the small is 1 cubic centimeter. The height of the large cylinder is 6cm. What is the height of the small one?
• Apr 23rd 2009, 11:55 PM
Peleus
Ok lets work through them.

Quote:

Originally Posted by Jubbly
A coffee store sold two different cans.Regular and large. Dimensions of the large can is twice the dimension of the regular can. If the regular can has a volume of 72 cubic inches, what is the volume of the large can?

Out of that we get a few things. Can(regular) = 72 cubic inches. Can(large) = Can(regular) * 2.

Or in algebra terms.

The regular can can equal x, the large can would then be 2x, if x is 72, find 2x.

72 * 2 = 144.

The large can is 144 cubic inches.

Quote:

Originally Posted by Jubbly
A sphere has a surfeace area of 6 square yards. The sphere is en;arged by a scale factor of 3 to produce a new sphere. what is the new surface area of the new sphere?
For this the answer I got was 18 square yards.

Quote:

Originally Posted by Jubbly
The Cylinders are similar. The Volume of the large cylinder is 64 cubic centimeters and the volume of the small is 1 cubic centimeter. The height of the large cylinder is 6cm. What is the height of the small one?

Well, the big cylinder is 64 times the small cylinder. In other words let the small cylinder be x, and the large 64x. If 64x is 6cm, what does x equal?
• Apr 24th 2009, 12:14 AM
Prove It
Quote:

Originally Posted by Peleus
Ok lets work through them.

Out of that we get a few things. Can(regular) = 72 cubic inches. Can(large) = Can(regular) * 2.

Or in algebra terms.

The regular can can equal x, the large can would then be 2x, if x is 72, find 2x.

72 * 2 = 144.

The large can is 144 cubic inches.

Well, the big cylinder is 64 times the small cylinder. In other words let the small cylinder be x, and the large 64x. If 64x is 6cm, what does x equal?

Oh no... no no no no no...

If the dimensions of a shape are magnified by a scale factor, then the AREA of that shape is magnified by the SQUARE of the scale factor, and the VOLUME of that shape is magnified by the CUBE of the scale factor.

So for Question 1.

$\displaystyle \textrm{Can}_{\textrm{Regular}} = 72\textrm{inches}^3$

Since the volume is magnified by the CUBE of the scale factor (which in this case is 2...)

$\displaystyle \textrm{Can}_{\textrm{Large}} = 2^3 \times 72\textrm{inches}^3$

$\displaystyle = 8 \times 72\textrm{inches}^3$

$\displaystyle = 576\textrm{inches}^3$.

For Question 2.

The scale factor is 3, so the AREA is magnified by the SQUARE of 3.

So $\displaystyle SA_{\textrm{old}} = 6\textrm{yards}^2$

$\displaystyle SA_{\textrm{new}} = 3^2 \times 6\textrm{yards}^2$

$\displaystyle = 9 \times 6\textrm{yards}^2$

$\displaystyle = 54\textrm{yards}^2$.

For Question 3.

The cylinders are similar, so their dimensions have been magnified by a scale factor. This means that their VOLUMES have been magnified by the CUBE of the scale factor.

So $\displaystyle V_{\textrm{Large}} = k^3 \times V_{\textrm{Small}}$

$\displaystyle 64\textrm{cm}^3 = k^3 \times 1\textrm{cm}^3$

$\displaystyle k^3\textrm{cm}^3 = 64\textrm{cm}^3$

$\displaystyle k^3 = 64$

$\displaystyle k = 4$.

Using this information

$\displaystyle h_{\textrm{Large}} = k \times h_{\textrm{Small}}$

$\displaystyle 6\textrm{cm} = 4 \times h_{\textrm{Small}}\textrm{cm}$

$\displaystyle h_{\textrm{Small}} = 1.5\textrm{cm}$.