Question

A cuboid box of dimensions 20cm*10cm*8cm was made of cardboard.From the front face 2 circles of diameter 7 cm and a rectangle of 8 cm*2 cm were cut out.Find total surface area of cuboid?

Answer 1

Question #25957

A cuboid box of dimensions $20\mathrm{cm}^*10\mathrm{cm}^*8\mathrm{cm}$ was made of cardboard. From the front face 2 circles of diameter 7 cm and a rectangle of $8\mathrm{cm}^*2\mathrm{cm}$ were cut out. Find total surface area of cuboid?

Solution: We find the total surface area of a cuboid box.

$$S = 2 \times (10 \times 8) + 2 \times (20 \times 8) + 2 \times (10 \times 20) = 160 + 320 + 400 = 880 \mathrm{cm}^2.$$

Now we find the area of the surfaces that were cut from the cuboid box:

$$S_1 = 3.14 \times (3.5)^2 = 38.465 \mathrm{cm}^2, \quad S_2 = 3.14 \times (3.5)^2 = 38.465 \mathrm{cm}^2,$$ $$S_3 = 8 \times 2 = 16 \mathrm{cm}^2.$$

Now we find the surface area that remained $(S_r)$:

$$S_r = S - S_1 - S_2 - S_3 = 880 - 38.465 - 38.465 - 16 = 787.07 \mathrm{cm}^2$$

Answer: $787.07 \mathrm{cm}^2$