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Artist 52 [7]
3 years ago
13

How many golf balls would fit in a 55 gallon drum? (One 2allon = 231 cubic inches; golf ball radius = .840 inches Volume of sphe

re = 4/3 * pi * r ^ 3
Mathematics
1 answer:
erastovalidia [21]3 years ago
5 0

5,082 balls  golf balls would fit in a 55 gallon drum.  

<u>Solution:</u>

Given,  

Radius of a golf ball = 0.840 inches

\text {Volume of the golf ball}=\frac{4}{3} \times 3.14 \times r^{3} [Pi = 3.14]

\rightarrow \frac{4}{3} \times 3.14 \times(0.840)^{3}=2.5 \text { inches }^{3} \\\\ \text { Volume of the gallon }=\text { number of gallons } \times \text { value of one gallon }

\rightarrow 55 \times 231 \text { cubic inches }=12705 \text { cubic inches }

\text { Number of balls fit }=\frac{\text { volume of the gallon }}{\text { volume of the golf ball }}

\rightarrow \frac{12705}{2.5}=5,082

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Step-by-step explanation:

Step 1: Sketch the problem as shown in the attached image.

The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.

It follows the equation x² + y² = 15².

The distance covered by Greg is given by <em>x mi</em>, and that of Erin is given by <em>y mi</em>.

Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>

Which by cross-multiplying gives <em>distance = speed × time</em>.

Let time taken to cover the distance be <em>t h</em>.

Given that Speed of Erin is 9 mph and that of Greg is 7 mph.

Hence, distance covered by Greg, x = 7 × t = 7t.

Distance covered by Erin, y = 9 × t = 9t.

Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for <em>time t.</em>

(7t)² + (9t)² = 15²

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(49 + 81)t² = 225

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