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A spherical balloon is inflated at a rate of 10 cm cube per sec what is the change in its radius when it's radius is 10 cm?
To find the change in the radius of a spherical balloon being inflated at a rate of 10 cm³/sec, we start with the formula for the volume of a sphere, ( V = \frac{4}{3} \pi r^3 ). The rate of change of the volume ( \frac{dV}{dt} ) is related to the rate of change of the radius ( \frac{dr}{dt} ) by the equation ( \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt} ). Substituting ( r = 10 ) cm and ( \frac{dV}{dt} = 10 ) cm³/sec, we find ( \frac{dr}{dt} = \frac{10}{4\pi (10)^2} = \frac{1}{40\pi} ) cm/sec. Thus, the change in radius when the radius is 10 cm is approximately ( \frac{1}{40\pi} ) cm per second.
What else can I help you with?
How do you calculate the radius of a balloon with an area of 1200 meters squared?
Assuming it is spherical: area = 4 x pi x radius2. Replace the area, and solve.
Why does the rate of change of the radius of a balloon slow down as the balloon gets bigger?
The volume of a balloon is like that of a sphere. So we use 4/3x Pix radius3 .Now plug in some numbers for V and see how radius changes. You will see if you go from a small volume to one a little larger, say .1 to .15, there is a pretty big change in the radius. Now try 1000 to 1000.15. You will see the change in the radius is much smaller.That is because of the fact the radius is cubed. I can't draw it here, but have a look at the graph of x cubed and that may shed some light on it.
The surface area of a balloon (which depends on the amount of air inside) is 2 square meters?
The surface area of a balloon is determined by its radius, which can be calculated using the formula for the surface area of a sphere: (A = 4\pi r^2). Given that the surface area is 2 square meters, we can rearrange the formula to find the radius. Solving for (r), we find that (r = \sqrt{\frac{A}{4\pi}} \approx 0.28) meters. This indicates that the balloon has a relatively small radius, contributing to its spherical shape.
What is the radius of a 32 foot spherical water tank?
volume of spherical = 4/3*Pi*Radius^3 = 4/3*3.14*32^3=137188
What is the spherical radius of 1 foot?
It is the distance from the centre to all points on the surface of a sphere with a radius of 1 foot.
How can we calculate the new volume of the balloon after it has been inflated?
To calculate the new volume of a balloon after it has been inflated, you can use the formula for the volume of a sphere, which is V 4/3 r3, where V is the volume and r is the radius of the balloon. Measure the radius of the inflated balloon and plug it into the formula to find the new volume.
How Can you find the volume of an inflated balloon?
To find the volume of an inflated balloon, you can measure its diameter using a ruler and then use the formula for the volume of a sphere, V = (4/3) * pi * r^3, where r is the radius (half of the diameter) of the balloon. Plug in the radius and calculate the volume. Alternatively, you can submerge the inflated balloon in a container of water and measure the water displacement to find the volume of the balloon.
Whenspherical balloon expands when it is taken from the cold outdoors to the inside of a warm house If its surface area increases 11.0 percent by what percentage does the radius of the balloon change?
If the surface area of a spherical balloon increases by 11%, the radius will increase by approximately 3.3%. This relationship is based on the formula that relates surface area to radius in a sphere (Surface Area = 4πr^2).
What is the radius of a 12 inch balloon?
Assuming the balloon is perfectly spherical and that the 12" you state refers to the diameter of the balloon then it is obviously 6". If you can't assume any of the above then your question cannot be answered.
Which doesnot change when spherical mirror is broken?
Its radius of curvature and its reflecting property
What is the volume of a balloon with a radius of 7 inches?
Assuming it is spherical (since it has a specific radius) then Volume = (4/3)pi*radius^3, so V = (4/3)pi*7^3 = 1436.76 cu. in.
Consider a balloon that is being inflated As the balloon increases in size the area of its surface increases Each time the balloon's diameter doubles what do you expect for the change in the area?
For any geometric figure, surface area is proportional to (linear dimensions)2 .As the balloon's diameter doubles, its area increases by the factor of (2)2 = 4 .
How do you calculate the radius of a balloon with an area of 1200 meters squared?
Assuming it is spherical: area = 4 x pi x radius2. Replace the area, and solve.
The surface area of a spherical balloon is 175 cm2 If the length of the radius was six times as large what would the surface area be?
this is funny cause i took an online test with this question
Why does the rate of change of the radius of a balloon slow down as the balloon gets bigger?
The volume of a balloon is like that of a sphere. So we use 4/3x Pix radius3 .Now plug in some numbers for V and see how radius changes. You will see if you go from a small volume to one a little larger, say .1 to .15, there is a pretty big change in the radius. Now try 1000 to 1000.15. You will see the change in the radius is much smaller.That is because of the fact the radius is cubed. I can't draw it here, but have a look at the graph of x cubed and that may shed some light on it.
The surface area of a balloon (which depends on the amount of air inside) is 2 square meters?
The surface area of a balloon is determined by its radius, which can be calculated using the formula for the surface area of a sphere: (A = 4\pi r^2). Given that the surface area is 2 square meters, we can rearrange the formula to find the radius. Solving for (r), we find that (r = \sqrt{\frac{A}{4\pi}} \approx 0.28) meters. This indicates that the balloon has a relatively small radius, contributing to its spherical shape.
How do you find the area of a balloon?
You mean the surface area, right? Assuming the balloon is approximately spherical, you can measure the diameter, divide by two to get the radius & plug that into this formula.A=¾πr²Where A is the area, r is the radius and π is the ratio of the circumpherence to the radius of a circle. 3.14 or 22/7 are good approximations to π, also a decent calculator will have a better approximation built in. To look it up search for "pi" (that's the Greek letter's name).
