Answer:
Part a) The Labeled part of the Can ⇒ 263.76 cm^2
Part b) The Surface Area of the Can is ⇒ 340.69 cm^2
Part c) The Volume of the Can is ⇒ 38.465 * 12 = 461.58 cm^2
Explanation:
~ If the dimensions of this can is 12 centimeters by 7 centimeters... ~
Part a)
1. Now a can is in the shape of a cylinder, thus the Base would act as a circle. That being said, 7 centimeters acts as the diameter of this circle.
2. If we were to unravel the middle of the can, it would be that this circular portion turns out of be a rectangle, with dimensions of the height of the cylinder, by the circumference of the Base of the cylinder. The circumference can be calculated by πd where d is the diameter ⇒ 3.14 * 7 ⇒ 21.98 cm. Thus the dimensions of this middle part of the can is 21.98 by 12 ⇒ 21.98 * 12 ⇒ 263.76 cm^2.
The Labeled part of the Can ⇒ 263.76 cm^2
Part b)
1. We know previously, that 7 centimeters acts as the diameter of this circle, so the radius must be half of that, which is 7/2 ⇒ 3.5 cm. Now we can apply the area of a circle formula πr^2 where r ⇒ radius, such that: 3.14 * ( 3.5 )^2 ⇒ 3.14 * 12.25 ⇒ 38.465 cm^2.
2. Knowing that the Base of this can is 38.465 cm^2, multiply this value by 2 to get the surface area of the two bases, provided they are equivalent: 38.465 * 2 ⇒ 76.93 cm^2
3. We know that this labeled section of the can is ⇒ 263.76 cm^2. This means that The Surface Area of the Can is ⇒ 263.76 + 76.93 = 340.69 cm^2
Part c )
The volume of the can is calculated by Base * height. We know from the previous questions that the Base ⇒ 38.465, and the height was given to be 12 centimeters. This means that The Volume of the Can is ⇒ 38.465 * 12 = 461.58 cm^2