It's been troubling me!

Geometry Level 2

A solid sphere is cut into identical pieces by three mutually perpendicular plane passing through its center. Increase in total surface area of all the pieces with respect to the total surface area of the original sphere is

225 % 225 \% 250 % 250 \% 150 % 150 \% 175 % 175 \% 125 % 125 \%

Achal Jain by Achal Jain , 19, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Marta Reece
Apr 11, 2017

Area of a sphere is 4 π R 2 4\pi R^2 .

Each of the three cut adds area equal to π R 2 \pi R^2 to each of the two sides of the cut, so the total increase is 3 × 2 × π R 2 3\times2\times\pi R^2 .

As a percentage of the original it comes to 6 π R 2 4 π R 2 = 3 2 = 150 \frac{6\pi R^2}{4\pi R^2}=\frac{3}{2}=150 %.

3 Helpful 0 Interesting 0 Brilliant 1 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...