Do you play football?

Geometry Level 5

The picture above shows a football having 12 congruent regular pentagons & 20 congruent regular hexagons (all of equal sides) on its surface. Find out the correct value (up to three decimal points) of solid angle (in ste-radian) subtended by each pentagon at the center of the football.


The answer is 0.295072263.

View wiki
Harish Chandra Rajpoot by Harish Chandra Rajpoot , 30, 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

Puresky Walker
Apr 26, 2015

A quick estimate: Ω 5 : Ω 6 ≈ S 5 : S 6 \Omega_5:\Omega_6 \approx S_5:S_6

S 5 = 5 a 2 / ( 4 tan ⁡ ( π / 5 ) ) S_5=5a^2/(4\tan(\pi/5))

S 6 = 3 3 a 2 / 2 S_6=3\sqrt{3}a^2/2

12 Ω 5 + 20 Ω 6 = 4 π 12\Omega_5+20\Omega_6=4\pi

Ω 5 = π 3 + 6 3 tan ⁡ ( π / 5 ) ≈ 0.2978 \Omega_5=\frac{\pi}{3+6\sqrt{3}\tan(\pi/5)} \approx 0.2978

Here's a solution: HCR's Theory .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

@Puresky Walker: The link you provided is greatly helpful to all. Thanks for posting this link.

mukul avasthi - 4 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...