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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.
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.
Jul 19, 2024 · The surface area of a sphere with a diameter of 8 cm is 201.06 cm 2. To obtain this result, follow these steps: Multiply the diameter by itself to get the diameter squared: d 2 = 8 2 = 64 cm 2. Multiply the diameter squared by pi to obtain the sphere's surface area: A = π × d 2 = π × 64 cm 2 ≈ 201.06 cm 2. Verify the result using our area ...
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.
Surface Area of Sphere Examples. Example 1: If the radius of a sphere is 20 feet, find its surface area. (Use π = 3.14). Solution: Given, the radius 'r' of the sphere = 20 feet. The surface area of the sphere = 4πr 2 = 4 × π × 20 2 = 5024 feet 2. ∴ The surface area of the sphere is 5024 feet 2.
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 ...
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 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.
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.
