Math mini-contest problem for Day 5 on D.Buzz for April 2021 π
Math mini-contest problem for Day 5 on D.Buzz for April 2021 π
Turner is designing a spearhead which is a right circular cone. The distance of the spearhead's point to the base is 1 foot and the apex angle is 15Β°. What is the volume of the spearhead?
0
0
0.000
The answer is 0.018 cubic feet.
h = 1 foot
c = h / cos(7.5 degrees) = 1.00863 (radius is half of 15 degrees)
r = sqrt(c^2-h^2) = 0.13165
Volume = β Ο (r^2) (h) = 0.018 cubic feet.
With my Scholl remembers about 0.074 ft^3 ? π€
I believe @jfang003 got it correctly - I won't try this time :)
Posted via D.Buzz
Answer for Day 5 Math Problem
Equivalent answers in other cubic units or in terms of Ο shall also be accepted.
Solution
To be able to get the volume of a cone, we first need to get its radius. The formula for the volume of a cone is
volume = Ο * radiusΒ² * height / 3
, and we already have the height in the given.To get the radius, we can "flatten" the cone to form two triangles where one is triangle ABC, where:
Our priority now is to get the measure of side AC (or simply side b), which is also the radius of the base of the cone.
Based on the details above, we have the measure of three angles and one side of the triangle. We can use the Law of Sines to get the measure of side b given side a, angle B, and angle a.
b / sin (B) = a / sin (A)
b / sin (7.5Β°) = 1 / sin (90Β°)
b = sin (7.5Β°)
b β 0.1305
The radius of the base of the cone is approximately 0.1305 feet. We just need to insert the radius and the height to the formula for the volume of the cone, so we get:
V = Ο * rΒ² * h / 3
V β Ο * (0.1305)Β² * 1 / 3
V β 0.0178
The volume of the cone (which is Turner's spearhead in the original problem) is approximately 0.0178 cubic feet.
Winner: @jfang003 π
The 1 HIVE award has been sent to @jfang003's HIVE account. π°
Participant mentions: @holovision, @ahmadmanga (@ahmadmangazap), @eturnerx (@eturnerx-dbuzz), @dkmathstats, @paultactico2, and @appukuttan66 π€
Special mentions: @dbuzz, @chrisrice, @jancharlest, and @mehmetfix π€―