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What is the total surface area of a cone whose radius is 24 cm and height is 10 cm?
Question

What is the total surface area of a cone whose radius is 24 cm and height is 10 cm?

A.

3249.76 cm²

B.

4261.23 cm²

C.

3771.43 cm²

D.

3924.61 cm²

Correct option is C

Given:
Radius (r) = 24 cm
Height (h) = 10 cm
Total Surface Area = ?
Formula Used:
Total Surface Area of Cone = πr(r+l)\pi r (r + l)​​
where l=r2+h2 l = \sqrt{r^2 + h^2}​ (slant height)
Solution:
l=242+102l=576+100=676=26l = \sqrt{24^2 + 10^2}\\l = \sqrt{576 + 100} = \sqrt{676} = 26​​
Total Surface Area=π×24×(24+26)=π×24×50=1200πTotal Surface Area=1200×2273771.43 cm2\text{Total Surface Area} = \pi \times 24 \times (24 + 26) \\= \pi \times 24 \times 50 = 1200 \pi\\\text{Total Surface Area} = 1200 \times \frac{22}{7} \approx 3771.43 \, \text{cm}^2\\​​

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