Answer:
1) True, True, False
Rewritten statement: 46,013.86 cm³ of water was used to fill 40 balloons
2) False, True, True
Rewritten statement: The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.
3) True, False, True
Rewritten statement: The volume of all the basketballs is 13,467.62 in³
Step-by-step explanation:
Question 1
[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Given:
Substituting the given radius into the formula:
[tex]\begin{aligned}\implies \sf V & = \sf \dfrac43 \pi (6.5)^3\\\\& =\sf \dfrac{2197}{6} \pi \\\\& = \sf 1150.35\: cm^3 \:(nearest\:hundredth)\end{aligned}[/tex]
[tex]\textsf{Volume of 40 balloons}=\sf 40 \times \dfrac{2197}{6} \pi=46013.86\:cm^3\:(nearest\:hundredth)[/tex]
Rewritten statement: 46,013.86 cm³ of water was used to fill 40 balloons
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Question 2
[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Earth
Given:
- diameter = 4.8 cm ⇒ r = 2.4 cm
Substituting the given radius into the formula:
[tex]\implies \sf V= \sf \dfrac43 \pi (2.4)^3[/tex]
[tex]\implies \sf V=57.91\:cm^3\:(nearest\:hundredth)[/tex]
Rewritten statement:
The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.
Saturn
Given:
- diameter = 45.6 cm ⇒ r = 22.8 cm
Substituting the given radius into the formula:
[tex]\implies \sf V= \sf \dfrac43 \pi (22.8)^3[/tex]
[tex]\implies \sf V=49647.02\:cm^3\:(nearest\:hundredth)[/tex]
Difference between models= 49,647.02 - 57.91 = 49,589.11 cm³
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Question 3
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
Substituting the given values into the formula:
[tex]\implies \sf V=\pi (21)^2(54)[/tex]
[tex]\implies \sf V=23814\pi[/tex]
[tex]\implies \sf V=74813.89\:in^3\:(nearest\:hundredth)[/tex]
[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Given:
- diameter = 9.5 in ⇒ r = 4.75 in
- 30 basketballs
[tex]\begin{aligned}\textsf{Volume of all 30 basketballs} &=\sf 30 \times \dfrac{4}{3}\pi (4.75)^3\\ & =\sf 13467.62\:in^3\:(nearest\:hundredth)\end{aligned}[/tex]
Rewritten statement: The volume of all the basketballs is 13,467.62 in³
Empty space in the container = volume of container - volume of basketballs
⇒ 74813.89 - 13467.62 = 61,346.27 in³
