Question 133

The total surface area of a right pyramid on a square base of side 10 cm with height 12 cm is:

Solution

Height = $$h=12$$ cm and side of base = $$s=10$$ cm

=> Radius of base = $$r=\frac{10}{2}=5$$ cm

Perimeter of base = $$4\times10=40$$ cm

Area of base = $$10\times10=100$$ $$cm^2$$

Thus, slant height = $$l=\sqrt{r^2+h^2}$$

=> $$l=\sqrt{(5)^2+(12)^2}$$

=> $$l=\sqrt{25+144}=\sqrt{169}=13$$ cm

Thus, curved surface area of pyramid = $$\frac{1}{2}\times$$ Perimeter of base $$\times$$ slant height

= $$\frac{1}{2}\times40\times13=260$$ $$cm^2$$

$$\therefore$$ Total surface area of pyramid = Curved surface area + Area of base

= $$260+100=360$$ $$cm^2$$

=> Ans - (B)


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