Question

Here are two closed containers and four balls just fit into each container. Each ball has a diameter of 60mm. Which container has the smaller surface area? You must show your working. Mathswatch

Answer 1

Answer:

"A is smaller"

Step-by-step explanation:

The full question is attached.

Surface area of cylinder:

The formula is  $SA=2\pi r^2 + 2\pi r h$

where r is the radius and h is the height

Here, radius would be 30 since balls have diameter 60 and radius is half of that.

Also height is the diameter of 4 balls line-by-line, so height is 60*4 = 240

Now, plugging into the formula, we get:

$SA=2\pi r^2 + 2\pi r h\\SA=2\pi (30)^2 + 2\pi (30) (240)\\SA=50,868$

Surface Area of rectangular prism:

The surface area of rectangular prism is the area of all the rectangular surfaces (6 of them).

Area of top and bottom = (60+60)*(60+60) * 2 = 120*120 * 2 = 28,800

Area of 2 sides = 2 * (60*120) = 14,400

Area of front and back = 2 * (60*120) = 14,400

Total Surface Area = 28,800 + 14,400 + 14,400 = 57,600

Thus, cylinder has smaller surface area.

"A is smaller"

Answer 2

Answer:

2827.433388 x 2 = 5654.866776

188.4955592 x 240 = 45238.93421

50893.80099

60 x 120 x 4 = 28800

120 x 120 x 2  = 28800

28800 + 28800 = 57600

'A is smaller'

I have put that into Mathswatch and this is the correct answer