### Video Transcript

The diagram below shows the net of
a cylinder where π΄π΅πΆπ· is a rectangle with π΄π΅ equals 20 centimeters and π΄π·
equals 44 centimeters. The net is formed into a cylinder
by joining line segment π΄π΅ with line segment π·πΆ, then folding over the two
circles of radii seven centimeters to make the top and the base. What is the total surface area of
the cylinder? Use π as 22 over seven.

Weβve been given the net of a
cylinder and asked to calculate its total surface area. The total surface area of any solid
is simply the sum of the areas of all its faces, which can easily be found from its
net as this is a two-dimensional representation of the solid. From the given net, we can identify
that a cylinder has a rectangular face, which forms the curved surface of the
cylinder when the net is folded, and two circular faces, which form its ends. Weβve been given the dimensions of
each of these shapes. So we can calculate their areas by
applying standard formulae.

The area of a rectangle is found by
multiplying its length by its width. So the area of this rectangle is 44
multiplied by 20. The area of a circle is π
multiplied by its radius squared. The two circles at either end of
the cylinder are congruent, and both have a radius of seven centimeters. So their combined area is two
multiplied by π multiplied by seven squared.

Weβve been told to use the value 22
over seven as an approximation for π. So before we evaluate, weβll make
this substitution. 44 multiplied by two is 88, so 44
multiplied by 20 is 880. For the second part of the
expression, we can cancel a factor of seven from the numerator and denominator,
leaving two multiplied by 22 multiplied by seven. Thatβs 14 multiplied by 22. And using any method for
multiplying two two-digit numbers without a calculator, we find that this is equal
to 308. Finally, we sum these two values
and include the units for this area, which are square centimeters.

Weβve found that the total surface
area of the given cylinder using π as 22 over seven is 1,188 square
centimeters.