Question

what is the lateral area, surface area, and volume of right cylinder with a radius of 5 centimeters and a height of 22 centimeters

Answer 1

Step-by-step explanation:

the volume is

base area × height

the base area is a circle, and the area of a circle is

pi×r²

in our case the volume is

pi×5²×22 = pi×25×22 = 550pi = 1,727.875959... cm³

the surface area is the sum of

2 circles (top and bottom) = 2× pi×5²

the lateral area

the lateral area (the "mantle wall" of the cylinder) you can imagine to be cut open and then placed flat on a table.

in this case you can see it is just a rectangle, with the cylinder height being the width, and the circle circumference being the length.

the circle circumference is

2×pi×r = 2×pi×5 = 10pi = 31.41592654... cm

so, the lateral area is

22 × 31.41592654... = 691.1503838... cm²

the surface area is then

691.1503838... + 2×pi×25 = 691.1503838... + 50pi =

= 848.2300165... cm²