Answer for Day 3 Math Problem

8.36 cubic inches🎯

Equivalent answers in other cubic units, in either fractional or decimal format, shall be accepted.
 

Solution

The problem is about a spherical cap, which is formed by a plane cutting a sphere. In the original problem, the spherical cap is the water content of the hemisphere.

The volume of a spherical cap given the radius of the base of the cap and the radius of the sphere can be obtained using the following formula.

V = π * h² * (3r - h) / 3

where

• r = radius of the sphere (or the height of the hemisphere)
• h = height of the spherical cap

However, it is important to take note that the height of the spherical cap is not equal to the radius of the sphere (unless otherwise indicated). We still need to get the value of h using the values of r (which is 8 inches) and b (which is 3 inches).

To get the height of the spherical cap, we should use the formula that makes use of the radii of the sphere and the base of the spherical cap as posted here.

h = r - √(r² - b²)

which will then produce

h = 8 - √(8² - 3²) ≈ 0.5838

That value is nicely displayed on the Desmos graph screenshot below (as inspired by @minus-pi)!

Using the values r = 8 and h = 0.5838 for V = π * h² * (3r - h) / 3, we get

• V = π * h² * (3r - h) / 3
• V = π * 0.5838² * (3 * 8 - 0.5838) / 3
• V ≈ 8.357481828

The volume of the spherical cap, which is the water in the bowl in the original problem, is approximately 8.36 cubic inches. 🤓

This example would help! 🤔

Winner: @minus-pi 🏅

1 HIVE has been sent to @minus-pi's Hive account. Additionally, since he was able to point out the error in my solution, I also awarded him with 1 extra HIVE!

• I can't determine how @jfang003 got his answer, since he provided minimal to no solution! 🤯

Participants: @holovision, @ahmadmanga (@ahmadmangazap), @eturnerx (@eturnerx-dbuzz), @paultactico2, @dkmathstats, and @appukuttan66 🤓
Special mentions: @chrisrice, @jancharlest, and @mehmetfix 🤯