Volume of sphere

The formula for the volume of a sphere is V = 4/3 π r³, where V = volume and r = radius. The radius of a sphere is half its diameter. So, to calculate the surface area of a sphere given the diameter of the sphere, you can first calculate the radius, then the volume. Created by Sal Khan and Monterey Institute for Technology and Education. Since the Volume of a Sphere is V=(4/3)πr^3, we are using the rational number 4/3 to give us the EXACT solution. Notice however that in this video, after Mr. Khan does his substitution, he uses his calculator to find an APPROXIMATE solution of V=(4/3)π(7)^3=1436.8. Had the problem specified to find the EXACT volume, then we would just substitute, V=(4/3)π(7)^3 and simplify to V=(4/3)π(343)=(1372/3)π, where we do NOT perform the division. Great question!! The 4/3 isn't so obvious and requires some work to derive. Consider the following two figures: Figure 1: the top half of a sphere with radius r. Figure 2: a cylinder with radius r and height r, but with a cone (with point on bottom at the center of the cylinder's bottom base) with radius r and height r removed from it. From the volume formulas for a cylinder and a cone, the volume of Figure 2 is pi r^2 * r - (1/3) pi r^2 * r = (2/3) pi r^3. Now we need to compare the areas of the horizontal cross sections of Figure 1 and Figure 2 at any given height h above the bottom. Once we show that these cross sections have equal areas at every height, then Cavalieri's principle would imply that the v...

Enter the known measure (i.e., either the radius or the volume) into the respective input box and the unknown measure will be calculated. That is, If you enter the radius as input, then the volume of the sphere will be calculated. If you enter the volume as input, then the radius of the sphere will be calculated. The volume of a sphere refers to the amount of space the sphere occupies. A sphere is a three-dimensional round solid figure in which all points on its surface are at a fixed distance from a fixed point. The fixed distance is known as the radius of the sphere and the fixed point is known as the center of the sphere. The volume of a sphere or the space occupied by it can be calculated using a standard formula. It is written as: When the radius is known the volume of a sphere can be written as: Volume of a sphere, \(V=\frac\) ; where ‘V’ is the volume of the sphere. Consider a sphere of radius r . The radii of the cylinder and cone are also r and their height is h , which is taken as 2r . Volume of Sphere, \( V_=2:3:1 \) Hence the volume of the sphere is twice the volume of the cone and the volume of the cylinder is thrice the volume of the cone. Example 1: Find the volume of a sphere whose diameter is 12 cm. (Take \( \pi=\frac \) \( ~~~~~~~~~~~~~~~~~~r=15 \) feet. Therefore, the radius of the sphere is 15 feet. Let the initial volume of the sphere of radius \( r \) be \( V \) and the final volume of the sphere after doubling the radius be \( V_1 \) . The radius now...

Sphere A sphere is a three-dimensional round-shaped object. Unlike other three-dimensional shapes, a sphere does not have any vertices or edges. All the points on its surface are equidistant from its center. In other words, the distance from the center of the sphere to any point on the surface is equal. There are many real-world objects that we see around us which are spherical in shape. Our planet Earth is not in a perfect shape of a sphere, but it is called a spheroid. The reason it is called a spheroid is that it is almost similar to a sphere shape. 1. 2. 3. 4. 5. 6. What is a Sphere? In • Radius: The length of the • Diameter: The length of the line segment from one point on the surface of the sphere to the other point which is exactly opposite to it, passing through the center is called the • Circumference: The length of the great circle of the sphere is called its • Volume: Like any other three-dimensional object, a sphere also occupies some amount of space. This amount of space occupied by it is called its • Surface Area: The area occupied by the surface of the sphere is its Sphere Formulas A sphere shape consists of a radius, diameter, circumference, surface area, and volume. Considering a sphere to have a radius of 'r', the following table lists the important formulas of a sphere. Name Formula Diameter 2 × radius of the sphere Circumference 2πr, where Surface Area 4πr 2 Volume (4/3)πr 3 Sphere Surface Area The area covered by the outer surface of the sphere is know...

Volume of Hemisphere The volume of a hemisphere is the space occupied by the hemisphere. An object with a larger volume occupies more space. A hemisphere is a 3D object which is half of a full sphere, for example bowls, headphones, Igloo, domes in architecture, etc. Therefore, the volume of a hemisphere is half the volume of a sphere. Let us learn how to find the volume of the hemisphere with the help of a few solved examples and practice questions. 1. 2. 3. 4. Volume of a Hemisphere Formula The volume of a hemisphere is half the volume of a sphere, therefore, it is expressed as, Volume of hemisphere = 2πr 3/3, where r is the radius of the hemisphere. Let us see how the formula for the volume of a hemisphere is derived. Since a hemisphere is half of a sphere, we can divide the volume of a sphere by 2 to get the volume of its hemisphere. Now considering that the radius of a Volume of the sphere can be calculated using the formula, Volume of Sphere = 4πr 3/3. So, the volume of a hemisphere = 1/2 of 4πr 3/3 = 1/2 × 4πr 3/3 = 2πr 3/3 How to Find the Volume of a Hemisphere? The volume of a hemisphere is calculated using the formula, Volume of hemisphere = 2πr 3/3. So, let us find the volume of a hemisphere which has a radius of 7 units. • Step 1: Note the • Step 2: Substitute the value of the radius in the formula, Volume of hemisphere = 2πr 3/3 and represent the final answer with cubic units. • Step 3: After substituting the value of r = 7, we get, Volume of hemisphere = 2πr 3...

• • • • • • Volume of a Sphere – Introduction Have you ever wondered, “I can draw a circle, but I cannot draw a sphere? Why?” This is because a circle is a two-dimensional figure and does not have volume, whereas a sphere is a three-dimensional shape with no edges or vertices. That means its points lie in space. Hence, you cannot draw it. This is the reason we always find the volume of a sphere to calculate the amount of space it occupies. Scroll ahead to learn about the volume of a sphere formula, the derivation of the sphere volume formula, some solved examples, facts, and more. What Is the Volume of a Sphere? Wondering how we can find the volume of a sphere? Hold on, we will get to that, but first, understand what the volume of a sphere means. The volume of a sphere is the measure of three-dimensional space occupied by a sphere. It depends on the sphere’s radius, which is half the diameter (the longest line inside the sphere that passes through the center of the sphere). That means if the radius of the sphere changes, its volume changes too! The volume of a sphere is measured in cubic units, such as $m^3$, $cm^3$, and so on. What Is the Formula to Find the Volume of a Sphere? How do you find the volume of a sphere given that “r” is the radius of the sphere? The volume of a sphere equation is as follows: The volume of a sphere $= \frac \times 3.14 \times 7 \times 7 \times 7 = 1436.02$ $cm^3$ Practice Problems Correct answer is: 38,808,000 liters The given values are, r $...