Expert: Ahmed Salami - 10/30/2008

Question
Mr Salami,
Can you please look at the following problems and kindly provide me with the correct answer and in doing so can you please  explain what I did wrong. Your help in this matter will be greatly appreciated .

For #1 I chose (b)

1. How many square feet of paper are needed to cover a cube with a side 10 inches long
(A) 4.17 sq ft  (b) 6.94 sq ft  (c) 80.52 sq ft
(d) 86.40 sq ft

For #2 I chose (d)

2. A cylindrical container has a base area 100m² and is 12m high. If the container is 1/3 filled with water .What is the volume of the water in the container.
(A) 300m³ (b)400m³ (c)600m³ (d) 1200m³


Answer
Hi Akmed,
I dont know what you've done so i cant tell you what you did wrong but hopefully you'll see for yourself.
1)1 inch = 1/12 ft
A cube with each length l has six equal surfaces, the area of each surface being l². The total surface area of the cube is therefore
A = 6l²
This is also the area of paper required to completely cover the cube.
but l = 10 inches
     = 10/12 ft
     = 5/6 ft
A = 6(5/6)²
 = 6(25/36)
 = 25/6
 = 4.17 sq ft

2)The volume of a cylinder with radius r and height h is
V = #r²h
where # is the constant pi
But area of the (cylindrical) base is
A = #r²
And so,
V = Ah
For A = 100m² and h = 12m
V = 100.12
 = 1200m³
But the container is only 1/3 filled so the volume of water it contains is 1200/3 = 400m³

Regards.