Use the formulas for arc length and surface area and the equation x^2+y^2=R^2 (a)... to derive...

Use the formulas for arc length and surface area and the equation x^2+y^2=R^2

(a)... to derive the formula for the surface area of a sphere with radius R

(b)... to derive the formula for the circumference of a circle with radius R

Expert Solution

Using Implicit differentiation, we have to first find out dy/dx and then using the formula to find the surface area of the sphere with radius R, we have got the surface area to be equal to

Similarly, using dy/dx from part (a), first the circumference of the semicircle is to be evaluated using the formula of Arc length and then doubling it would give the circumference of the circle.

milcah answered 2 years ago

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