Video Transcript
The total surface area of a cube is
𝐴 is equal to six 𝐿 squared. Find 𝐴 when 𝐿 is equal to
one-half of a centimeter.
In this question, we are given a
formula for the total surface area of a cube, that is, the sum of the areas of each
of its six faces. We want to use this formula to find
the total surface area of a cube whose sides have lengths one-half of a
centimeter. To do this, we need to start by
substituting 𝐿 is equal to one-half into the given formula for the total surface
area. This gives us that 𝐴 is equal to
six times one-half squared.
In the order of operations, we need
to evaluate the exponents before the multiplication, so we need to square
one-half. We can do this by recalling that we
can square fractions by squaring their numerators and denominators separately. So, 𝑏 over 𝑐 all squared is equal
to 𝑏 squared over 𝑐 squared. We can set 𝑏 equal to one and 𝑐
equal to two to obtain that 𝐴 is equal to six times one squared over two
squared.
We can then evaluate each of the
squares. We know that one squared is one
times one, which is equal to one, and two squared is two times two, which is equal
to four. This leaves us with six times
one-quarter. We can multiply these values to
obtain six over four. We can then cancel the shared
factor of two in the numerator and denominator to get three-halves. We cannot simplify this fraction
any further, and we know that this is an area with lengths measured in
centimeters. So we can give this the units of
square centimeters.
Hence, the total surface area of a
cube with sides of length one-half a centimeter is three-halves square
centimeters.
