Finding the surface area of the following cans to the nearest square container

Question

How can I find the surface area of the following cans to the nearest square centimeter?

a) Coffee can (r) radius= 7.6 cm, height = 16.3 cm

b) Soup can (r) radius= 3.3 cm, height = 10 cm

PLEASE HELP!

Answer 1

Each can is a right cylinder. The surface area of a right cylinder is the sum of the areas of the ends and the area of the column. Each end is a circle, area = pi x r² . The column of the cylinder is a rectangle of width equal to the circumference of the circle, c=2 x pi x r, formed by the ends and height equal to the height of the cylinder. To visualize this, take a piece of paper - it is a rectangle, right? Now roll it so that it forms a round column - cylinder - with open ends.

Now let’s put this all together: The coffee can has a radius of 7.6 cm. It has two ends, each of which is a circle. The area of a circle of radius 7.6 cm is a=3.14 (7.6 cm)² =1378.4 cm², multiply by two since there are two ends = 2756.77 cm² for the area of the ends. The surface area of the column of the cylinder is the area of the rectangle (area = w x h) it forms if cut and flattened: its width, the circumference of a circle of radius 7.6 cm, is c = 2 x 3.14 x 7.6 cm = 47.7 cm times the height, 16.3 cm = 777.97 cm².  Add the areas of the ends and the column, 2756.77 cm² +777.97 cm² = 3534.7 cm². If you are asked to round to the nearest whole number, the answer would be 3535 cm², 

Solved in the same way, the soup can has a surface area of 275.7 cm². See if you can follow the process above to get this answer.

Answer 2

If r=radius of the can and h=height,

then the surface area of the top is πr² and the area of the bottom is the same.

The surface area of the sides is 2πrh.

You can use these formulae to answer the questions.