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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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\huge \boxed{\mathbb{QUESTION} \downarrow}

  • Solve ⇨ 4 - (- 4)^-3

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\sf \: 4 - ( - 4 ) ^ { - 3 }

Calculate -4 to the power of -3 and get -1/64.

\dashrightarrow \sf \: ( - 4) ^{3 }  \\  =   \sf-\frac{1}{4 ^{3} }  \\  =  \sf  - \frac{   1}{4}  \times  -  \frac{  1}{4}  \times   - \frac{  1}{  4}  \\  =  \sf \:   - \frac{  1}{64}

Come back to the equation & substitute -4³ as -1/64.

\sf \: 4-\left(-\frac{1}{64}\right)  \\

The opposite of -1/64 is +1/64.

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The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

<h3>What is the distance in kilometres covered by the satellite after 8 revolutions?</h3>

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Read more on circumference of a circle;

brainly.com/question/20489969

#SPJ1

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