Question Video: Finding the Surfacer Area of a Cube with Lengths Given as Fractions | Nagwa Question Video: Finding the Surfacer Area of a Cube with Lengths Given as Fractions | Nagwa

Question Video: Finding the Surfacer Area of a Cube with Lengths Given as Fractions Mathematics • First Year of Preparatory School

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The total surface area of a cube is 𝐴 = 6𝐿². Find 𝐴 when 𝐿 = 1/2 cm.

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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.

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