Tennis balls with a diameter of 2.5 in. are packaged 3 to a can. The can is a cylinder. Find the volume of the space in the can that is not occupied by tennis balls. Assume that the balls touch the sides, top, and bottom of the can. Round your answer to the nearest hundredth. What is the volume not occupied by balls?

Answers

Answer 1

Answer: a) First we calculate the volume of each ball:

$\boxed{V=(4\pi r^3)/(3)}\n \n \boxed{V=(4*(3,14)*(1.25)^3)/(3)=8,177 \ square \ inch}$

b) Now we calculate the volume of tree balls:

$\boxed{V_T=3*8,177=24.531 \ square \ inch}$

c) Now we calculate the volume of cylinder:

c1) Base area:

$\boxed{A_b=\pi r^2}\n \n \boxed{A_b=3,14*(1,25)^2=4.906 \ square \ inch}$

c2) Cylinder height

$\boxed{h=3*(2.5)=7.5 \ inch}$

c3) Cylinder Volume:

$V_C=A_b*h\n \n \boxed{V_C=4.906*7.5=36.795 \ cubic \ inch}$

d) Finally we calculate the internal space:

$\boxed{\boxed{s=36.795-24.531= 12,264\ cubic \ inch}}$

Answer 2

Answer: $d=2.5 \ in \n \n r=(d)/(2)=(2.5)/(2)=1.25 \ in \n \n \pi=3.14 \n \nVolume \ of \ a \ Cylinder : \n \nV = \pi r^2 h$

$h=3\cdot d = 3*2.5 = 7.5 \ in \n \nV_(c) = 3.14\cdot (1.25)^2\cdot 7.5 = 23.55 * 1.5625=36.80 \ in^3$

$The \ volume \ of \ tree \ balls : \n \n V_(3b)= 3 \cdot (4)/(3) \pi r^3 = 4\pi r^3 \n \nV_(3b)=4\cdot 3.14\cdot (1.25)^3= 12.56\cdot 1.9531 \approx 24.53 \ in^3 \n \nV_(c)-V_(3b)=36.80-24.53 =12.27 \ in^3 \n \n Answer : \ The \ volume \ not \ occupied \ by \ balls \ it \ 12.27 \ in^3$

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Answers

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Answer:

61 miles per hour

Step-by-step explanation:

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Answers

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Answers

Good job !! There all correct !

Yes don't forget if you need to simplify do so .

length of a room is 3 times its breadth and height is 4.6 m.if the total cost of carpeting the floor of a room at the rate of Rs. 60 per square meter is Rs. 4500,Find the total cost of papering the 4 walls at the rate of Rs. 6.

Answers

The total cost of papering the 4 walls is Rs. 1104

Step-by-step explanation:

The given is:

The length of a room is 3 times its breadth
Its height is 4.6 m
The total cost of carpeting the floor of a room at the rate of Rs. 60 per square meter is Rs. 4500

We need to find the total cost of papering the 4 walls at the rate of Rs. 6

Assume that the breadth of the room is x m

∵ The length of the room is 3 times its breadth

∵ The breadth of the room is x m

∴ The length of the room is 3 x m

∵ The floor of the room is shaped a rectangle

- Area of the rectangle = length × breadth

∴ The area of the floor = (3 x) × (x) = 3 x²

∵ The rate of the carpeting is Rs. 60 per square meter

- Multiply the area of the floor by 60 to find the total cost of carpeting

∴ The total cost of carpeting = 3 x²(60) = 180 x²

∵ The total cost of carpeting the floor is Rs. 4500

- Equate the two sides of total cost to find x

∴ 180 x² = 4500

- Divide both sides by 180

∴ x² = 25

- Take √ for both sides

∴ x = 5

∴ The breadth of the room = 5 m

∵ The length of the room is 3 x

∴ The length of the room = 3(5) = 15 m

The four walls of the room has dimensions length × height , breadth × height , length × height , breadth × height ⇒ (each two opposite walls have same dimensions)

∵ The length = 15 m , breadth = 5 m , height = 4.6 m

∴ The area of the four walls = 2(15 × 4.6) + 2(5 × 4.6)

∴ The area of the four walls = 138 + 46

∴ The area of the four walls = 184 m²

∵ The rate per meter square of papering is Rs. 6

- Multiply the area of the four walls by 6 to find the total cost

of papering

∴ The total cost of papering = 184 × 6

∴ The total cost of papering = Rs. 1104

The total cost of papering the 4 walls is Rs. 1104

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You can learn more about the word problem in brainly.com/question/10557938