Surface Area: This is Calc Right?

Geometry Level 3

A painter is painting a house both inside and out. He has 10 paint cans, each of which can paint an area of $\pi$ sq. units. How many paint cans will he need to paint the $\textbf{entire}$ roof if the roof is modeled by rotating the graph of $y=\sqrt{1-x^2}$ about the x axis $360^{\circ}$ where $0\leq x\leq 1$

This is for the problem writing party on surface areas

The answer is 4.

1 solution

Brian Charlesworth
Mar 3, 2016

The given curve describes the portion of a radius $r = 1$ circle lying in the first quadrant, which upon rotation about the $x$ -axis creates a hemispherical shell. As both the inside and outside of this shell is to be painted, the total surface area will be just that of an entire sphere of radius $1$ , which has a surface area of $4\pi r^{2} = 4\pi$ sq. units. Thus precisely $\boxed{4}$ cans of the given coverage will be required.

Surface Area: This is Calc Right?

This is for the problem writing party on surface areas

The answer is 4.

1 solution

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