The circumference of the base of a right circular cylinder is 176 cm and it is 1 m high.

Question

The circumference of the base of a right circular cylinder is 176 cm and it is 1 m high. Find the lateral surface area of the cylinder.

Answer 1

Lateral surface area of a cylinder can be calculated using the formula: L (lateral surface area) = 2π x R (radius) x H (height)

 

Basically, if you take apart the rectangular portion of the cylinder and made it flat, that is the lateral surface area.

 

Now, since you are given the circumference of the base of the right circular cylinder, that is the diameter not the radius. Luckily, we can find the radius knowing that the diameter is just twice the value of the radius. So, to find the radius "R" we must divide or half the value of the diameter: R = D (diameter)/2 = 176 cm / 2 = 88 cm. So, the radius is 88 cm: R = 88 cm.

 

Now we know the radius and we know the height! We can now find the lateral surface area, but wait we have one more little step to do before we can calculate it. As you see the radius is in centimeters "cm" and the height is in meters "m". In order to properly find the lateral surface area we must change the units to equal values, by changing the radius to meters: R = 88 cm = 88 x 10^-2 m = 0.88 m. If you don't want your answer in meters but want centimeters instead you can change the height in a similar fashion: H = 1 m = 1 x 10² cm = 100 cm.

 

After changing the unit to either "cm" or "m" we can now calculate "L": 

In centimeters: L = 2π x (88 cm) x (100 cm) = 55292 cm²

In meters: L = 2π x (0.88 m) x (1 m) = 5.5292 m²

 

The answer looks nicest in meters, so that's what I would suggest using although both answers are correct! Notice how you must also multiply the units, which will give you an answer in cm squared or m squared.

Answer 2

The formula for the lateral surface area of cylinder is C x h, where C is the circumference and h is the height.

 

But when you do the multiplication, all the measurements have to be in the same units.

 

176 cm = 1.76 m, because there are 100 cm in a meter.

 

So the area of this cylinder is just 1.76 x 1 = 1.76 m2