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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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\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{C = 2πr} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{226.08 = 2(3.14)\red{r}} \\ \\ \: \: \: \: \: \: \: \: \large \tt{ \frac{226.08}{6.28} = \cancel\frac{6.28 \red{r}}{6.28} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt\green{C = 36}}\end{gathered}

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6.28

226.08

=

6.28

6.28r

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To check:

\begin{gathered} \small\begin{array}{|c|}\hline \bold{circumference }\\ \\ \tt{C = 2πr} \\ \tt{C = 2(3.14) (36\:cm) } \\ \tt{C = 2(113.04\:cm) } \\ \underline{\tt \green{C = 226.08\:cm }} \\ \hline \end{array} \end{gathered}

circumference

C=2πr

C=2(3.14)(36cm)

C=2(113.04cm)

C=226.08cm

FINAL ANSWER

If Mary's Bicycle has a circumference of 226.08 cm then the radius is 36.

\boxed{ \tt \red{r = 36}}

r=36

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