0
$\begingroup$

enter image description here

The sphere in the figure is of radius 15 cm. How do I find the surface area of the shaded part of the sphere in figure 1? Please help!

$\endgroup$
0

2 Answers 2

1
$\begingroup$

As you see the inner triangle has sides $20cm$ and $15cm$ and is right angled, so the third side (that from O to the top of the triangle) must be $25cm$ (it's pythagorean). Also as the radius of the circle is $15cm$ you would have that the height of the triangle is $40cm$.

This means that the the width of the triangle $20cm$ up from the base is half of the base (as it's half-way to the top).

Then you use the formula for the area of a trapezoid. It becomes $A = {30+60\over 2}20 cm^2$

$\endgroup$
1
  • $\begingroup$ Figure 1 is the side view of figure 2. It is a 3D problem. But I have been thinking if I can use similar figure to solve it ...the sphere has more than half of it immersed in water... $\endgroup$
    – user256670
    Feb 2, 2016 at 19:14
1
$\begingroup$

Wikipedia: Spherical Cap

The formula you need for the surface area of the shaded portion of the sphere is $A=2\pi rh$. You have $r=15$ and $h=20$, so $A=600\pi\,cm^2$.

$\endgroup$
2

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .