Question 68

A cone has a radius of 20 cm and height 21 cm, then the total surface area (in cm$$^2$$)of the cone is:(Take $$\pi = \frac{22}{7}$$)

Solution

A cone has a radius of 20 cm and height 21 cm.

Let's assume the radius, height, and slant height of a cone is r, h, and l respectively.

As we know that $$l^2\ =\ r^2\ +h^2$$

$$l^2\ =\ (20)^2\ + (21)^2$$

$$l^2\ =\ 400\ +441 = 841$$

$$l = 29$$ cm

total surface area of cone = $$\pi\ r\left(r+l\right)$$

= $$\frac{22}{7}\times\ 20\times\left(20+29\right)$$

= $$\frac{22}{7}\times\ 20\times49$$

= $$22\times\ 20\times7$$

= 3080 $$cm^2$$

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