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A prism has a square base whose side is 8 cm. The height of the prism is 80 cm. The prism is cut into 10 identical parts by 9 cuts which are parallel to the base of the prism. What is the total surface area (in cm2) of all the 10 parts together?

A prism has a square base whose side is 8 cm. The height of the prism is 80 cm. The prism is cut into 10 identical parts by 9 cuts which are parallel to the base of the prism. What is the total surface area (in cm2) of all the 10 parts together? Correct Answer 3840

Total surface area of the prism before cutting = Curved S.A + 2 × (Base Area)

⇒ (Perimeter of base × Height) + 2 × (Base Area)

⇒ (4 × 8 × 80) + (2 × 8 × 8)

⇒ 2688 cm2

Now when the prism is cut into 10 identical sides, the base area will only increase.

Increase in Base Area = 18 × (Base Area) = 18 × 64 = 1152 cm2

∴ Total surface area of all the 10 parts together = 2688 + 1152 = 3840 cm2

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