【How-to】Is it possible for a sphere to have the same numerical value for the surface area and volume

Can volume be equal to surface area?

Surface area is a two-dimensional measure, while volume is a three-dimensional measure. Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm.

Is the volume and surface area of sphere are numerically the same then its radius is?

The volume and surface area of a sphere are numerically equal. … The radius of the sphere. Solution: The radius of the sphere is 3 units.

Will the surface area of a cube ever have the same numerical value as the volume of a cube?

Originally Answered: The numerical value of the volume of the cube is equal to the numerical value of it’s total surface area. What is the length of it’s side? The numerical value of the volume of the cube is equal to the numerical value of it’s total surface area.

Is it possible for a sphere to have the same volume and surface area?

The formula for the surface area of a sphere is S = 4πr², and we are given in this case that 4πr² = Nπ. We now need to find the radius r of a sphere in which both the volume and the surface area of the sphere are numerically equal. A volume cannot equal and area; just like a length can’t equal a time.

What is the ratio between the volume of a sphere and volume of a circumscribing right circular cylinder?

So, the ratio of the volume of sphere to the volume of the cylinder is 2: 3 .

How does the surface area of a sphere change when the radius is tripled?

In the case of a sphere if the radius is tripled the surface becomes (3r)^2 or 9-fold. In other words the surface area will increase by 800%.

How does the volume of a sphere relate to the volumes of other solids?

The volume V of a sphere is four-thirds times pi times the radius cubed. The volume of a hemisphere is one-half the volume of the related sphere. Note : The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

How are cube and sphere different?

A sphere has circular cross-sections however sliced, and all such cross-sections that pass through the centre of the sphere are identical. A cube has no circular cross-sections but six square faces (necessarily, three mutually perpendicular pairs of parallel faces).

Does a sphere have more volume than a cube?

And no, they don’t have same volume either. So for this condition sphere SA is more then cube.

How does the volume of a sphere work?

Why is the rate of change of the volume of a sphere not constant?

Explain why the rate of change of the radius of a sphere is not constant even though dV/dt is constant. I understand why the first one is true: the volume is dependent on r^2 and thus even if dr/dt is constant, dV/dt is not constant because the volume is exponentially related to radius.

What is the relationship between the volume of a cylinder and a sphere?

What is the relationship between the volume of the sphere and the volume of the cylinder? (Answer: The sphere takes up two-thirds of the volume of the cylinder.)

What is are needed to find the volume of a sphere?

To calculate the volume of a sphere, use the formula v = ⁴⁄₃πr³, where r is the radius of the sphere. If you don’t have the radius, you can find it by dividing the diameter by 2. Once you have the radius, plug it into the formula and solve to find the volume.

Why is there a 4 3 in the volume of a sphere?

Since the cylinder/cone and hemisphere have the same height, by Cavalieri’s Principle the volumes of the two are equal. The cylinder volume is πR3, the cone is a third that, so the hemisphere volume is 23πR3. Thus the sphere of radius R has volume 43πR3.

What is a formula for a sphere?

Answer: The equation of a sphere in standard form is x² + y² + z² = r². Let us see how is it derived. Explanation: Let A (a, b, c) be a fixed point in the space, r be a positive real number and P (x, y, z ) be a moving point such that AP = r is a constant.

How do you find the volume of a sphere without the radius?

Why is a sphere 2/3 of a cylinder?

If the height of the cylinder equals the diameter of the sphere, , and if the diameter of the cylinder is equal to the diameter of the sphere, , so the volume is . This is half as much again as the volume of the sphere, which is two-thirds of the volume of the cylinder.

How do you find the radius of a sphere if you know the volume?

Answer: To find the radius of a sphere with the volume, we use the formula: r = (3V/4π)

How do you find the radius of a sphere in real life?

The radius is half the diameter, so use the formula r = D/2. This is identical to the method used for calculating the radius of a circle from its diameter. If you have a sphere with a diameter of 16 cm, find the radius by dividing 16/2 to get 8 cm. If the diameter is 42, then the radius is 21.

How do you find the radius of a sphere without knowing the diameter?

How to Calculate the Radius of a Sphere?

Radius = Diameter / 2.
Radius = ⎷[Surface Area / (4 π)]
Radius = ³⎷[3 * Volume / (4 π)]