I have no idea. Please help with this question I suck at graphs

Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.

jenyasd209 [6]

The total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm.

Radius of 1 sphere = 6.5 cm

We know that the volume of the sphere is given by 4/3 π r³

We will take the radius as 6.5 cm and π as 22/7

Now we will find the volume : 4/3 ×22/7×6.5³ = 1150.81 cubic cm.

Volume of 40 such spheres = 40 × 1150.81 = 46032.38 cubic cm.

The radius of all the spheres are 46032.38 cubic cm.

A sphere is a geometrical entity with three dimensions that resembles a two-dimensional circle. A sphere is a group of points in three dimensions that are all situated at the same r-distance from one another.

The supplied point is the sphere's center, while the letter r stands for the sphere's radius which is half the diameter. The earliest known allusions to spheres are found in the works of two ancient Greek mathematicians.

Therefore total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm .

Disclaimer: The complete question is : Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.Find the total volume of water required.

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3 0

1 year ago

A helicopter leaves an airport and flies south at 180 mi/h. Thirty minutes later, an airplane leaves the airport and follows the

stira [4]

Answer:

36 minutes

Step-by-step explanation:

helicopter 1 is ahead of helicopter 2 by 90 miles

the difference in their speeds is 150 mph

90/150=3/5 of hour

3/5*60=36 minutes

8 0

3 years ago

12. A man planted trees on both sides of

netineya [11]

Answer:

1000 trees : Can u plz give me the brainliest answer? Plz!!!!!!!!!!!!!!!

Step-by-step explanation:

5000m divided by 5m = 1000 trees

Have a nice day!!!!!! :-)

3 0

3 years ago

Read 2 more answers

Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.