Question

If the total surface area of a cube is 864 cm², find its lateral surface area.​

Answer 1

Answer:

Total surface area of cube=864cm²

6l²=864cm²

l²=864/6

l=√144=12cm

Lateral surface area of cube=4l²

4×12×12=576cm²

Step-by-step explanation:

Answer 2

$\mathtt{\huge{\fbox{SOLUTION}}}$

Given ,

The total surface area of cube = 864 cm²

We know that , the TSA of cube is given by

$\mathtt{\fbox{TSA \: of \: cube = 6 \times {(side)}^{2} }}$

Substitute the known values , we obtain

$\sf \hookrightarrow 864 = 6 \times {(side)}^{2} \\ \\\sf \hookrightarrow {(side)}^{2} = 144 \\ \\ \sf \hookrightarrow side = 12 \: cm$

Hence , the side of cube is 12 cm

Now , the volume of cube is given by

$\mathtt{\fbox{TSA \: of \: cube = 4 \times {(side)}^{2} }}$

Substitute the value , we get

$\sf \hookrightarrow Volume = 4 × 12 × 12 \\ \\\sf \hookrightarrow Volume = 576 \: \: {cm}^{3}$

Hence , the volume of cube is 576 cm³