Answer for Day 5 Math Problem

0.0178 cubic feet 🎯

Equivalent answers in other cubic units or in terms of π 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 = π * radius² * 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:

• angle B is equal to half of the vertex angle, which is 7.5°;
• angle C is 90° (which will give us 82.5° as the measure of angle A);
• side BC (or simply side a) has a length of 1 foot.

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 (7.5°) = 1 / sin (90°)
b = sin (7.5°)
b ≈ 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 = π * r² * h / 3
V ≈ π * (0.1305)² * 1 / 3
V ≈ 0.0178

The volume of the cone (which is Turner's spearhead in the original problem) is approximately 0.0178 cubic feet.

Winner: @jfang003 🏅

The 1 HIVE award has been sent to @jfang003's HIVE account. 💰

• @minus-pi knew that @jfang003's answer was correct, but he was just late in answering on his own! 😅
• Thanks to @bencwarmer for trying to answer the question, but I don't know how he got the answer. His answer is roughly 4.2 times the correct answer. 🤔

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