The surface area of a cube is 864 in2. What is the area of one face of this cube?

2 answers:

6 0

A cube has six identical faces, so the surface area is six times the area of one face.

Let x be the area of one face.
$6x=864 \\ x=\frac{864}{4} \\ x=144$

The area of one face of this cube is 144 in².

Ganezh [65]4 years ago

3 0

$S=6a^{2} \\ \\ 6a^{2}=864 \\ \\ a^{2}=144$

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Find AD. Show how you got your answer.

stealth61 [152]

Notice the picture below
the AD line is a bisector, cutting the 36 degrees A in half,
18 and 18 degrees each half

notice the tickmarks, the triangle is an isosceles,
if those two sides are equal, so are the angles they make
down below with the base

now, the base is 8, AD is bisecting that too, to 4 and 4

now, using the Law of Sines

$\bf \textit{Law of sines}
\\ \quad \\
\cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\
----------------------------\\\\
\cfrac{sin(18^o)}{4}=\cfrac{sin(72^o)}{\overline{AD}}\implies \overline{AD}=\cfrac{4\cdot sin(72^o)}{sin(18^o)}$

keep in mind, the angles are in degrees, so, when taking the sines, make sure your calculator is in Degree mode