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Question

If the volume of a square-based prism is 250cm2 and height is 10cm, find the total surface area.

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Solution

The general formula for volume of prism is V=s2h where s is the base and h is the height.

Since volume of the prism is V=250 cm2 and the height h=10 cm, therefore, the area of base is:

V=s2h250=10s2s2=25010=25s=25=5

Now, the perimeter P of the prism is P=4×side, therefore, the perimeter of prism with side 5 cm is P=4×5=20 cm.

The general formula for the total surface area of a right prism is TSA=Ph+2B where P represents the perimeter of the base, h is the height of the prism and s is the base.

TSA=Ph+2s2=(20×10)+(2×25)=200+50=250 cm2

Hence, the total surface area is 250cm2.

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