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Solved Examples. Example 1– Calculate the cost required to paint a football which is in the shape of a sphere having a radius of 7 cm. If the painting cost of football is INR 2.5/square cm. (Take π = 22/7) Solution. We know, The total surface area of a sphere = 4 π r 2 square units. = 4 × (22/7) × 7 × 7. = 616 cm2.
Volume of the sphere (V) = 4 π r 2. = 4 x 3.14 x 12 x 12. = 1808.64. Hence area of the sphere is 1808.64 feet 2. Example 3: A spherical ball has a surface area of 2464 sq. cm. Find the radius of the ball, correct to 2 decimal places (using pi = 22/7) Solution: Step 1: Surface area of a sphere = 2464 cm 2.
3 days ago · The radius of the sphere whose volume and surface area are equal is 3 units. To find this answer, follow these steps: Let the radius of this sphere we seek be r. Equate the sphere's volume to its surface area to get the equation: 4⋅π⋅r 3 /3 = 4⋅π⋅r 2. Divide both sides by 4⋅π⋅r 2 to get: r/3 = 1. Multiply both sides by 3 to get ...
Example: Find the surface area of a spherical ball that has a radius of 9 inches. Step 1: Note the radius of the sphere. Here, the radius of the ball is 9 inches. Step 2: As we know, the surface area of sphere = 4πr 2, so after substituting the value of r = 9, we get, surface area of sphere = 4πr 2 = 4 × 3.14 × 9 2 = 4 × 3.14 × 81 = 1017.36.
3 days ago · A sphere is a perfectly round geometrical 3-dimensional object. It can be characterized as the set of all points located distance r r (radius) away from a given point (center). It is perfectly symmetrical, and has no edges or vertices. A sphere with radius r r has a volume of \frac {4} {3} \pi r^3 34πr3 and a surface area of 4 \pi r^2 4πr2.
Jun 11, 2023 · The surface area of a sphere is the entire region covered by its outer round surface. It is also the curved surface area of a sphere. Like all other surface area it is expressed in square units such as m 2, cm 2, and mm 2. We will learn how to find the surface area of a solid sphere. The equations are given below. Formulas. The basic formula is ...
Oct 4, 2023 · Calculator online for a the surface area of a capsule, cone, conical frustum, cube, cylinder, hemisphere, square pyramid, rectangular prism, triangular prism, sphere, or spherical cap. Calculate the unknown defining side lengths, circumferences, volumes or radii of a various geometric shapes with any 2 known variables. Online calculators and formulas for a surface area and other geometry problems.
The surface area of a sphere is 4πr 2. Since a hemisphere is half of a sphere, its surface area, S, is half the surface area of a sphere plus the area of the circular base (shown in gray) created by intersection of the plane and sphere: S = 4πr 2 /2 + πr 2 = 3πr 2. where r is the radius of the hemisphere.
The surface area of a sphere is given by the formula. Area. =. 4. π. r. 2. Where r is the radius of the sphere. In the figure above, drag the orange dot to change the radius of the sphere and note how the formula is used to calculate the surface area.
Derivation. Archimedes, the famous Greek polymath, found that the surface area of a sphere is equal to the curved surface area of a cylinder with a radius equal to the sphere's radius and height equal to the sphere's diameter. Now, the curved surface area of a cylinder is given by –. A_c = 2 \pi r h Ac = 2πrh.
The surface area of the sphere is 289.5 \mathrm{~cm}^2 \, \text{(1dp)}. Example 2: surface area of a sphere. Find the surface area of a sphere with the diameter of 42 \mathrm{~mm}. Write your answer to the nearest square millimeter. Write down the formula. To answer the question, use the formula for the surface area of a sphere: \text{Surface area}=4 \pi r^2 .
Example 1: surface area of a sphere given the radius. Find the surface area of the sphere below. Write your answer to 1 decimal place. Write down the formula. To answer the question we need to use the formula for the surface area of a sphere: \text{Surface area}=4 \pi r^2 . 2 Substitute the given values into the formula.
The surface area of a sphere is measured to be 100π square meters. What is the diameter of the sphere in meters? Solution: First, we will plug the surface area value into the formula and solve for the radius r. SA = 4πr 2. 100π = 4πr 2. 25 = r 2. r = 5. Now that we have the radius, let's convert it to diameter.
Radius, r =14 cm. By the formula, Surface area of a sphere = 4πr 2. On substitution, we get, SA = 4 x 3.14 x 14 x 14. = 2,461.76 cm 2. Example 2. The diameter of a baseball is 18 cm. Find the surface area of the ball. Solution.
Why Is the formula for surface area of sphere equal to 4pir^2? And applying its formula to find the surface area. Created by Devashish Phadnis.
In the above example, the radius of the sphere is 8 cm. If the diameter is given, divide the diameter by 2 to get the radius. Step 2: Now, surface area of sphere = 4 π r 2, so after substituting the value of r = 8, we get, surface area of sphere = 4 π r 2 = 4 × 3.14 × 8 2 = 4 × 3.14 × 64 = 803.84. Step 3:
Jan 16, 2024 · 4πr 2. r = 7. 4 * π * 7 2. 49 * 4 * π. 196π. Answer: Surface Area = 615.75 centimeters 2, or 615.75 square centimeters. 8. Understand surface area. The surface area of a sphere is the area covering the outside of the sphere -- think of it as the rubber covering a kickball or the surface of the earth.
The surface area of the sphere pictured on the left is: A = 4π ⋅ r2 A = 4π ⋅ 32 A = 36π = 113.1 A = 4 π ⋅ r 2 A = 4 π ⋅ 3 2 A = 36 π = 113.1.
A sphere is defined by three axes, x-axis, y-axis and z-axis. The region occupied by a circle is simply an area. The formula of the area is πr2. A sphere has a surface area covered by its outer surface, which is equal to 4πr2. It does not have any volume.
6 days ago · Surface area of 1 Surface area of 2 Surface area of 1 Surface area of 2. =. Solution: 4π(2x × 2x) 4π(10x × 10x) 4 π ( 2 x × 2 x) 4 π ( 10 x × 10 x) =. 1 25 1 25. Hence, the required ratio of their surface areas is 1:25. Example : Find the radius of the sphere if the surface area of the sphere is 300 inch2.
The surface area formula for a sphere is 4 x π x (diameter / 2) 2, where (diameter / 2) is the radius of the sphere (d = 2 x r), so another way to write it is 4 x π x radius 2. Visual on the figure below: A sphere's surface area can be calculated just by knowing its diameter, or radius (diameter = 2 x radius). π is, of course, the well-known mathematical constant, about equal to 3.14159. To find the SA simply multiply 4 times 3.14159 times the radius square.
Jun 22, 2023 · So, the radius of the sphere = diameter 2 = 10 cm 2 = 5 cm. We know that the surface area of a sphere is calculated as. A = 4 π r 2. So, the surface area of a sphere of radius 5 cm = 4 × 22 7 × 5 × 5 c m 2. = 4 × 22 × 5 × 5 7 cm. = 314.28 c m 2. Q.3. The surface area of a sphere is 201 sq m.
Jun 11, 2024 · Example: Find the surface area of a sphere of radius 7 cm. Step 1: Note the radius of the given sphere. Here, the radius of the sphere is 47 cm. Step 2: We know that the surface area of a sphere = 4πr2. So, substitute the value of the given radius in the equation = 4 × (3.14) × (7)2 = 616 cm2.
Jan 27, 2024 · The surface area of a sphere, SA = 4\Pi\:r^{2}unit^{2} Volume of sphere, V = \frac{4}{3}\Pi\:r^{3}unit^{3} Diameter of sphere, D = 2r, where r is the radius. Surface Area Of A Sphere. The surface area of a sphere is defined as the total area covered by the surface of a sphere in a three-dimensional space. The formula of the surface is given by:
