The document contains four applications involving calculations of surface area and volume: 1) Finding the height of an aquarium tank given its volume and base dimensions. 2) Comparing the surface area and volume of a can and box to determine which holds more juice. 3) Calculating the surface area of a gift to see if wrapping paper is large enough. 4) Determining which of two pizza sauce cans is a better buy based on volume per dollar.

1. SURFACE AREA AND
VOLUME
APPLICATIONS
November 17, 2015

2. Application I
 A standard 20-gallon aquarium tank is a
rectangular prism that holds approximately
4600 cubic inches of water. The bottom glass
needs to be 24 inches by 12 inches to fit on
the stand.

3. Application I
 Find the height of the aquarium to the nearest
inch.
24
inches
12
inches
 V = l x w x h
 4600 = (24) x (12) x h
 4600 = 288 x h
 16.0 inches = h
V = 4600
cubic
inches

4. Application I
 Find the total amount of glass needed in
square inches for the six faces.
24
inches
12
inches
16
inches
 TSA = 2(24)(12) + 2(12)(16) +
2(24)(16)
 TSA = 576 + 384+768
 TSA = 1728 in2
12
inches
24
inches

5. Application II
 Does the can or the box have a greater
surface area? a greater volume?
6 cm
9 cm
9 cm
5 cm
5 cm
Cylinder Square Prism

6. Application II
6 cm
9 cm
Surface Area of can
rhrTSA  22 2

)9)(3(2)3(2 2
 TSA
 5418 TSA
2
72 cmTSA 
2
2.226 cmTSA
9 cm
6 cm

7. Application II
Surface Area of box
)4()2( 2
shsTSA 
))9)(5(4()5*2( 2
TSA
18050TSA
2
230 cmTSA
9 cm
5 cm
5 cm
9 cm
5
5 cm

8. Application II
 Since 230cm2 > 288.2cm2, the box has a
greater surface area.
 Which container holds more juice?

9. Application II
6 cm
9 cm
Volume of can
hrV 2

)9()3( 2
V
)9)(9(V
3
81 cmV 
3
5.254 cmV 
9 cm
6 cm

10. Application II
Volume of box
hwlV **
9*5*5V
9*25V
3
225 cmV 
9 cm
5 cm
5 cm
9 cm
5
5 cm

11. Application II
 Since 254.5cm3 > 225cm3, the can has greater
volume.
 If the can and the box were the same price,
which one would you buy?

12. Application III
 A birthday gift is 55 cm long, 40 cm wide, and
5 cm high. You have one sheet of wrapping
paper that is 75 cm by 100 cm. Is the paper
large enough to wrap the gift? Explain.

13. Application III
 TSA =
2(55)(40)+2(55)(5)+2(40)(5)
 TSA = 4400 + 550 + 400
 TSA = 5350 sq cm
 A = 75 x 100
 A = 7500 sq
cm
5 cm
55 cm
40 cm
75 cm
100cm

14. Application IV
 If both of these cans of pizza sauce are
cylinders, which is the better buy?
20.5
cm
7.5 cm
11 cm
10 cm
$3.49
$1.09

15. Application IV
 V = πr2h
 V = π(5)2(20.5)
 V = π * 25 * 20.5
 V = 512.5 π cm3
 V = 1610.1 cm3
 = 461 cm3 per dollar
20.5
cm
10 cm
$3.49
49.3$
1.1610 3
cm

16. Application IV
 V = πr2h
 V = π(3.75)2(11)
 V = 154.7 π cm3
 V = 486.0 cm3
 = 446 cm3 per dollar
09.1$
486 3
cm
7.5 cm
11 cm
$1.09

17. Application IV
 Which jar would you buy?
Since 461 cm2 per dollar > 446 cm2 per
dollar, you should buy the first jar.