Question 26

The perimeter of base of a right circular cone is 88 cm. If the height of the cone is 48 cm, then what is the total surface area (in cm$$^{2})\ $$of the cone?

Solution

Let radius of cone = $$r$$ cm and height = $$h=48$$ cm

Perimeter of base = $$2\pi r=88$$

=> $$2\times\frac{22}{7}\times r=88$$

=> $$r=88\times\frac{7}{44}=14$$ cm

Slant height of cone = $$l=\sqrt{r^2+h^2}$$

=> $$l=\sqrt{196+2304}=\sqrt{2500}$$

=> $$l=50$$ cm

$$\therefore$$ Total surface area of cone = $$\pi r(r+l)$$

= $$(\frac{22}{7}\times14)(14+50)$$

= $$44\times64=2816$$ $$cm^2$$

=> Ans - (D)

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