Ask question

Ask question

All categories

3 years ago

5

The senior class want to play a practical joke on the principal, who was a former college basketball star. They want to fill his

office full of basketballs. The diameter of a basket ball is 9.5 inches. The dimensions for his office are 20 feet long, 18 feet wide and 12 feet tall. If you assume there is not furniture in the office, then approximately how many basketballs would it take to fill up his entire office to the ceiling? (Model the basketball as a sphere).

1 answer:

steposvetlana [31]3 years ago

6 0

The number of basketball that will fill up the entire office is <u>approximately 16,615.</u>

<em><u>Recall:</u></em>

Volume of a spherical shape = $\frac{4}{3} \pi r^3$

Volume of a rectangular prism = $l \times w \times h$

<em><u>Given:</u></em>

Diameter of basketball = 9.5 in.

Radius of the ball = 1/2 of 9.5 = 4.75 in.

Radius of the ball in ft = 0.4 ft (12 inches = 1 ft)

Dimension of the office (rectangular prism) = 20 ft by 18 ft by 12 ft

First, find the volume of the basketball:

Volume of ball = $\frac{4}{3} \pi r^3 = \frac{4}{3} \times \pi \times 4.75^3\\$

Volume of basketball = $448.92 $ in^3$

Convert to $ft^3$

$1728 $ in.^3 = 1 $ ft^3$

<em>Therefore,</em>

Volume of basketball = $\frac{448.92}{1728} = 0.26 $ ft^3$

Find the volume of the office (rectangular prism):

Volume of the office = $20 \times 18 \times 12 = 4,320 $ ft^3$

Number of basket ball that will fill the office = Volume of office / volume of basketball

<em>Thus:</em>

Number of basket ball that will fill the office = $\frac{4,320}{0.26} = 16,615$

Therefore, it will take approximately <u>16,615 balls</u><u> to fill up the entire office</u>.

Learn more here:

brainly.com/question/16098833

You might be interested in

8-c is at most -15 how do i translate this into a sentence?

emmainna [20.7K]

The largest number that 8c could be is -15

3 0

3 years ago

In ΔEFG, the measure of ∠G=90°, FG = 67 feet, and EF = 98 feet. Find the measure of ∠F to the nearest tenth of a degree.

Mama L [17]

Answer:

46.9 degrees is the answer

6 0

3 years ago

Hurry pls it’s very confusing

Jobisdone [24]

Answer:

1/4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

In a chemistry lab an experiment requires 500ml of one ingredient to be mixed with 1000 mL of another. how many ounces is the so

zavuch27 [327]

Answer:

50.72 us fl oz

Step-by-step explanation:

Given:

500 ml of ingredient to be mixed with 1000 ml of another ingredient.

$\therefore \textrm{Total solution contains} = 1500ml$

Now we need to convert ml into Ounces.

Formula:

$\texttrm{us fl oz} = ml \times 0.033814= 1500 \times0.033814 = 50.72 oz$

$\therefore \textrm{Total solution contains} = 50.72 ounces$

5 0

3 years ago

The indicated function y1(x is a solution of the given differential equation. use reduction of order or formula (5 in section 4.

Taya2010 [7]

Given a solution $y_1(x)=\ln x$ , we can attempt to find a solution of the form $y_2(x)=v(x)y_1(x)$ . We have derivatives

$y_2=v\ln x$
${y_2}'=v'\ln x+\dfrac vx$
${y_2}''=v''\ln x+\dfrac{v'}x+\dfrac{v'x-v}{x^2}=v''\ln x+\dfrac{2v'}x-\dfrac v{x^2}$

Substituting into the ODE, we get

$v''x\ln x+2v'-\dfrac vx+v'\ln x+\dfrac vx=0$
$v''x\ln x+(2+\ln x)v'=0$

Setting $w=v'$ , we end up with the linear ODE

$w'x\ln x+(2+\ln x)w=0$

Multiplying both sides by $\ln x$ , we have

$w' x(\ln x)^2+(2\ln x+(\ln x)^2)w=0$

and noting that

$\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x$

we can write the ODE as

$\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0$

Integrating both sides with respect to $x$ , we get

$wx(\ln x)^2=C_1$
$w=\dfrac{C_1}{x(\ln x)^2}$

Now solve for $v$ :

$v'=\dfrac{C_1}{x(\ln x)^2}$
$v=-\dfrac{C_1}{\ln x}+C_2$

So you have

$y_2=v\ln x=-C_1+C_2\ln x$

and given that $y_1=\ln x$ , the second term in $y_2$ is already taken into account in the solution set, which means that $y_2=1$ , i.e. any constant solution is in the solution set.

4 0

3 years ago