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The volume of a sphere is given by the formula 4/3 *pi*r^3 and the surface area is given by the formula 4*pi*r^2. If you know the volume of the sphere you can solve for the radius, then you can plug the resulting value into the surface area formula. For example, suppose I knew that the volume of a sphere was 25 cubic meters:
Set 25 equal to the voume formula:
4/3*pi*r^3 = 25
multiply both sides by 3/4 and divide both sides by pi:
r^3=pi*75/4
take the cube root of both sides:
r=(pi*75/4)^(1/3)
Now plug r into my formula for surface area:
4*pi*r^2 = 4*pi*((pi*75/4)^(1/3))^2
And I probably want a decimal approximation for the surface area, that is, I probably want to get rid of the pis and the fractional exponent, so I can plug 4*pi*((pi*75/4)^(1/3))^2 into a calculator to get 190.24385. Then a sphere with a volume of 25 cubic meters has a surface area of 190.24385 square meters.
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How to find the surface area and volume of a sphere with a given radius.?
Given a sphere of radius r, Surface area = 4{pi}r2 Volume = (4/3){pi}r3
What geometric shape has the smallest surface area for given volume?
A sphere
What solid shape minimises surface area?
the sphere has the smallest surface area for any given volume.
What is the volume of a shape with a surface area of ten cm?
depends on the shape... if its a sphere or a prism or what. You'll get different answers because they have different surface area to volume ratios. Sphere will give you the biggest volume for a given surface area.
What is the formula for the volume of a sphere in terms of surface area S?
Given the surface area, where S=surface area, the formula for finding the volume isV = √(S / 4pi)
How to find the surface area and volume of a sphere with a given radius.?
Given a sphere of radius r, Surface area = 4{pi}r2 Volume = (4/3){pi}r3
What geometric shape has the smallest surface area for a given volume?
A sphere
What geometric shape has the smallest surface area for given volume?
A sphere
What solid shape minimises surface area?
the sphere has the smallest surface area for any given volume.
What is the volume of a shape with a surface area of ten cm?
depends on the shape... if its a sphere or a prism or what. You'll get different answers because they have different surface area to volume ratios. Sphere will give you the biggest volume for a given surface area.
What is the formula for the volume of a sphere in terms of surface area S?
Given the surface area, where S=surface area, the formula for finding the volume isV = √(S / 4pi)
Why does a sphere have the lowest surface area to volume ratio?
A sphere has the lowest surface area to volume ratio compared to other shapes because it has the smallest surface area for a given volume. This is due to its symmetrical shape, which minimizes the surface area while maximizing the volume. The sphere's surface area is spread out evenly in all directions, making it more compact and efficient.
What is the answer for the hemisphere?
The answer for the hemisphere is half the volume of a sphere, which is given by the formula (2/3)πr³, where r is the radius. The surface area of a hemisphere is half the surface area of a sphere, given by the formula 2πr².
Why is a ball a sphere and not a cube?
A ball is a sphere rather than a cube because a sphere is the shape with the least surface area for a given volume. This is known as the isoperimetric inequality, which states that among all shapes with the same volume, a sphere has the smallest surface area. This property makes a sphere the most efficient shape for enclosing a given volume, which is why objects like balls, bubbles, and planets tend to form into spheres in nature. In contrast, a cube has more surface area for a given volume compared to a sphere, making it less efficient in terms of minimizing surface area.
What is the surface area of a sphere with a volume of 3500pi?
The surface area of a sphere with a volume of 3500pi is: 2,391 square units.
What does volume and surface area have in common?
The volume of a body and the surface area arerelated but not in a direct way. For a given volume, the smallest surface area of an object is seen then the object is a sphere. As the shape flattens from a sphere, so the surface area becomes larger. When the object approaches an infinitely small thickness, the surface area approaches and infinite size.
How do you find mass of a sphere when only radius is given?
Volume of a sphere = 4/3*pi*radius3 Surface area of a sphere = 4*pi*radius2
