Help i need it fast and i did not listen

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

lianna [129]

We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ = $\frac{4}{3}$ π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.

R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = π r² h
V₁ = 3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³

b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × V₂
Vₐ = 3 × $\frac{4}{3}$ π r³
Vₐ = 3 × $\frac{4}{3}$ 3.14 (6.5 cm)³
Vₐ = 3,449.3 cm³

c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V = $\frac{ V_{1}}{ V_{a} }$ ×100
V = $\frac{3,449.3}{5,173.9}$ ×100
V = 0.6666 ×100
V = 66.66%

4 0

3 years ago

Read 2 more answers

Let X denote a random variable which corresponds to the number of players in a team who get injured during a game. If we assume

Feliz [49]

Answer:

(a)

The values of X can be 0, 1, 2 , ..., 10 . So, X is a discrete random variable.

(b)

The distribution of X is Binomial distribution with the parameters n = 10 and p = 0.2

(c)

Probability that no one or one person will be injured = P(X = 0) + P(X = 1)

= 10C0 * 0.20 * (1 - 0.2)10-0 + 10C1 * 0.21 * (1 - 0.2)10-1

= 0.810 + 10 * 0.2 * 0.89

= 0.3758096

(d)

Average value of X = np

Average value of X = 10 * 0.2 = 2

(e)

Variance of X = np(1-p)

Variance of X = 10 * 0.2 * (1 - 0.2) = 1.6

(f)

Number of ways in which 2 people gets injured = 10C2 = 10! / ((10-2)! 2!) = (10 * 9) / (2 * 1) = 45

Assume the best player got injures, number of ways in which one people out of remaining 9 people gets injured = 9C1

= 9! / ((9-1)! 1!)

= 9

Probability that the best player got injured = Number of ways in which 1 people gets out of 9 and best person gets injured / Number of ways in which 2 people gets injured

= 9 / 45

= 0.2

4 0

3 years ago

Of the flowers in Bella’s garden, 9/12 are tulips. What percent of the flowers in the garden are not tulips? A: 75 B: 25 C: 30 D

Amiraneli [1.4K]

9/12 as a percentage is equal to 75%.

7 0

3 years ago

Elina and Gustavo leave Cayley H.S. at 3:00 p.m. Elina runs north at a constant speed

Andrej [43]

Answer:

the answer to your question is 'b'

8 0

3 years ago

Which numbers represent the measure of the sides of a right triangle?

Dominik [7]

Answer:

2.8, 4.5, 5.3

numbers represent the measure of the sides of a right triangle.

2.8²+4.5²=5.3²

7.84+20.25=28.09

28.09=28.09

8 0

3 years ago

Help i need it fast and i did not listen​

Help i need it fast and i did not listen