Question

Find the approximate increase in the total surface area of a cone when its height remains constant and the radius increases by 2% at the time when its radius is 8 cm and the height is 6 cm.

Answer 1

Answer:

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Answer 2

Answer:

Approximate increase in the total surface area of a cone = 16.22 cm^2.

                                                                                         

Step-by-step explanation:

Since we know that the total surface area of a cone = $\pi r(r+l)$

we have $l = \sqrt{r^{2}+h^{2}  }$...........................(1)

If r = 8 cm and h = 6 cm so l =10 cm.

Initial total surface area of a cone = 3.14 x 8 (8+10)=452.16 cm^2.

Now,radius increases by 2% and height remains constant.

New radius = 8.16 cm l = 10.12 cm using (1)

Now ,the total surface area of a cone = $\pi r(r+l)$

                                                              = 3.14 x 8.16 (8.16 +10.12)

                                                              =468.38 cm^2

Approximate increase in the total surface area of a cone = 468.38-452.16

                                                                                              =16.22 cm^2.