Question

p(7,12,10),q(8,8,1) and r(11,3,9)are three vertices of a cube. what is its surface area?​

Answer 1

The Surface area of cube =294.

Step-by-step explanation:

$\ Given \ vertices:\\\\P (7,12,10)\\q (8,8,1)\\r (11,3,2)\\\\\ Find:\\\\\ surafce \ area =?\\\\\ Solution:\\\\\ formula \ of \ distance \\\\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\\\\\ Calculate \ distance: \\\\pq=\sqrt{(8-7)^2+(8-12)^2+(1-10)^2}\\\\\rightarrow pq= \sqrt{1^2+4^2+(-9)^2}\\\\\rightarrow pq= \sqrt{1+16+81}\\\\\rightarrow pq= \sqrt{98}\\\\pr=\sqrt{(11-7)^2+(3-12)^2+(9-10)^2}\\\\\rightarrow pr= \sqrt{4^2+(-8)^2+(-1)^2}$

$\rightarrow pr= \sqrt{4^2+(-9)^2+(-1)^2}\\\\\rightarrow pr= \sqrt{16+81+1}\\\\\rightarrow pr= \sqrt{98}$

$qr=\sqrt{(11-8)^2+(3-8)^2+(9-1)^2}\\\\\rightarrow qr= \sqrt{3^2+(-5)^2+8^2}\\\\\rightarrow qr= \sqrt{9+25+64}\\\\\rightarrow qr= \sqrt{98}$

$\ all \ the \ length \ is \ same. \ So, \ let \ side \ is \ x\\\\ x\sqrt{2} = \sqrt{98}\\\\x= \frac{\sqrt{98}}{\sqrt{2}} = 7\\\\\ Surface \ of \ cube \ formula\ = 6a^2 \\\\\rightarrow 6(7)^2\\\\\rightarrow 6\times 49 \\\\\rightarrow 294$

Learn more:

• Surfaces area of cube: https://brainly.in/question/14799923