Four glass balls, each with a $2$ . $5$ inch radius, are placed in a box. If the remaining space is to be filled with cotton for padding, how much cotton is needed? Use $3$ . $14$ for $\pi$

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Area and perimeter: word problems

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Q. Four glass balls, each with a

2

5

inch radius, are placed in a box. If the remaining space is to be filled with cotton for padding, how much cotton is needed? Use

3

14

for

\pi

Calculate Volume of Sphere: First, we need to calculate the volume of one glass ball. The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$ , where $r$ is the radius.
Substitute Radius in Formula: Since the radius of each glass ball is $2.5$ inches, we substitute $r$ with $2.5$ inches in the volume formula. $\newline$ $V = \left(\frac{4}{3}\right)\pi(2.5)^3$
Calculate Volume of One Ball: Now we calculate the volume of one glass ball. $\newline$ $V = \frac{4}{3} \times 3.14 \times (2.5)^3$ $\newline$ $V = \frac{4}{3} \times 3.14 \times 15.625$ $\newline$ $V = 4.18666667 \times 3.14 \times 15.625$ $\newline$ $V \approx 206.15$ cubic inches
Calculate Total Volume of Four Balls: Next, we calculate the total volume of the four glass balls by multiplying the volume of one ball by four. $\newline$ Total volume of glass balls = $4 \times 206.15$ cubic inches
Find Remaining Space for Cotton: Perform the multiplication to find the total volume of the four glass balls. $\newline$ Total volume of glass balls = $824.6$ cubic inches
Find Remaining Space for Cotton: Perform the multiplication to find the total volume of the four glass balls. $\newline$ Total volume of glass balls = $824.6$ cubic inchesAssuming we know the volume of the box, we would subtract the total volume of the glass balls from the volume of the box to find the volume of the remaining space to be filled with cotton. $\newline$ However, the volume of the box is not given in the problem, so we cannot calculate the exact amount of cotton needed without this information.