Three tennis balls are packaged in a box as shown below. The box is 12.1 centimeters long, 3.5 centimeters wide, and 3.5 centimeters tall. Each ball is 3.3 centimeters in diameter. What is the volume of the empty space in the box?

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Three tennis balls are packaged in a box as shown below. The box is 12.1 centimeters long, 3.5 centimeters wide, and 3.5 centimeters tall. Each ball is 3.3 centimeters in diameter. What is the volume of the empty space in the box?

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Answer 1 · 2018-05-13T08:28:13

$91.8 c m^{3}$ $91.8 cm^3$

Explanation:

Volume of the box is $12.1 \times 3.5 \times 3.5 = 148.225 c m^{3}$ $12.1 xx 3.5 xx 3.5=148.225 cm^3$

Each ball is $\frac{4}{3} \times π \times {1.65}^{3} = 18.8165692 c m^{3}$ $4/3 xx pi xx 1.65^3=18.8165692 cm^3$

There are three balls $\Rightarrow 56.4497076 c m^{3}$ $=> 56.4497076 cm^3$

Subtract

$\Rightarrow 148.225 - 56.4497076 = 91.7752924 c m^{3}$ $=> 148.225-56.4497076=91.7752924 cm^3$

Answer 2 · 2018-05-13T08:45:24

$V_{empty space} = 91.775$ $V_"empty space"=91.775$ $c m^{3}$ $cm^3$

Explanation:

$V_{box} = l \cdot w \cdot h = 12.1 \cdot 3.5 \cdot 3.5 = 148.225$ $V_"box"=l*w*h=12.1*3.5*3.5= 148.225$ $c m^{3}$ $cm^3$

$V_{each ball} = \frac{4}{3} π r^{3} = \frac{4}{3} π {(\frac{3.3}{2})}^{3} = \frac{4}{3} π (\frac{35.937}{8})$ $V_"each ball"=4/3pir^3=4/3pi(3.3/2)^3=4/3pi(35.937/8)$ $c m^{3}$ $cm^3$

$V_{3 balls} = (\frac{35.937}{2}) π \approx 56.450$ $V_"3 balls"=(35.937/2)pi~~56.450$ $c m^{3}$ $cm^3$

$V_{empty space} = 148.225 - 56.450 = 91.775$ $V_"empty space"=148.225-56.450=91.775$ $c m^{3}$ $cm^3$

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Three tennis balls are packaged in a box as shown below. The box is 12.1 centimeters long, 3.5 centimeters wide, and 3.5 centimeters tall. Each ball is 3.3 centimeters in diameter. What is the volume of the empty space in the box?

2 Answers

Explanation:

Explanation:

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