HELP ME

Use 3.14 for
π

a) What is the area of the label of a can with dimensions as shown?

cm2

b) What is the total surface area of the can?

cm2

c) What is the volume of the soup can?

cm2

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

Step-by-step 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

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