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hram777 [196]
3 years ago
6

Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and the sides of the c

ylinder. The diameter of each ball is 13 cm.

Mathematics
1 answer:
lord [1]3 years ago
6 0

Answer:

a. 5177 cm³

b. 3,451 cm³

c. 67%

Step-by-step explanation:

Given:

Diameter of each ball (d) = 13 cm

Radius of the ball (r) = radius of the cylinder = ½(13) = 6.5 cm

Height of the cylinder (h) = the sum of the diameters of the 3 balls = 3(13) = 39 cm

a. Volume of cylinder = πr²h

Plug in the values

Volume of cylinder = π*6.5²*39 = 5176.56 ≈ 5177 cm³

b. Total volume of the three balls = 3(volume of 1 ball) = 3(volume of sphere) = 3(⁴/3πr³)

Plug in the value

Total volume of the 3 balls = 3(⁴/3*π*6.5³) = 3(1150.35) = 3,451.05 ≈ 3,451 cm³

c. % of volume of the container occupied by the 3 balls = total volume of the three balls / volume of cylinder × 100

Plug in the values

= 3,451/5177 × 100

= 66.6602279

≈ 67%

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If θ=0rad at t=0s, what is the blade's angular position at t=20s
babunello [35]
The attached figure represents the relation between ω (rpm) and t (seconds)
To find the blade's angular position in radians ⇒ ω will be converted from (rpm) to (rad/s)
              ω = 250 (rpm) = 250 * (2π/60) = (25/3)π    rad/s
              ω = 100 (rpm) = 100 * (2π/60) = (10/3)π    rad/s

and from the figure it is clear that the operation is at constant speed but with variable levels
            ⇒   ω = dθ/dt   ⇒   dθ = ω dt

            ∴    θ = ∫₀²⁰  ω dt  
 
while ω is not fixed from (t = 0) to (t =20)
the integral will divided to 3 integrals as follow;
       ω = 0                                          from t = 0  to t = 5
       ω = 250 (rpm) = (25/3)π            from t = 5   to t = 15
       ω = 100 (rpm) = (10/3)π            from t = 15 to t = 20

∴ θ = ∫₀⁵  (0) dt   + ∫₅¹⁵  (25/3)π dt + ∫₁₅²⁰  (10/3)π dt
     
the first integral = 0
the second integral = (25/3)π t = (25/3)π (15-5) = (250/3)π
the third integral = (10/3)π t = (25/3)π (20-15) = (50/3)π

∴ θ = 0 + (250/3)π + (50/3)π = 100 π

while the complete revolution = 2π
so instantaneously at t = 20
∴ θ = 100 π - 50 * 2 π = 0 rad

Which mean:
the blade will be at zero position making no of revolution = (100π)/(2π) = 50
















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3 years ago
Nina sells 95% of her cookies at a bake sale. She baked 120 cookies. How many did she sell?
adoni [48]

Answer:

114 cookies

Step-by-step explanation:

120×0.95=114

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2 years ago
The fastest NASCAR qualifying speed is 313 feet per second. How many miles per hour is that?
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213.41 mph.

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Multiply by 3600 ( seconds in an hour) and divide by 5280 (feet in a mile).

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3 0
3 years ago
Marissa has twice as much money as Frank. Christina has $20 more than Marissa. If Christina has $100, how much money does Frank
qwelly [4]

Answer:

a. Take a grid that shows represents the amount of money Frank has,

Say F,

( shown below ),

b. Since, Marissa has twice as much money as Frank,

So, the amount Marissa has = 2F

If M represents the amount Marissa has,

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c. Now, Christina has $20 more than Marissa,

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d.  The below diagram provides enough information to determine the value of the variable m

e. The amount Christina has = M + 20 = 2F + 20

According to the question,

2F + 20 = 100

2F = 80

F = 40

Hence, the amount frank has = $ 40,

Amount Marissa has = 2(40) = $ 80,

3 0
3 years ago
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