The surface area of a sphere is the total area covered by its outer surface.
Sphere Surface Area Formula
The standard formula to calculate the surface area (A) of a sphere with radius (\(r\)) is given by:
\(A = 4\pi r^2\)
Comparing with Options
Let's compare this standard formula with the given options:
- Option 1: \(\left(\frac{4}{3}\right)\pi r^2\) (This is related to the volume formula, not surface area)
- Option 2: \(\left(\frac{4}{5}\right)\pi r^2\)
- Option 3: \(\left(\frac{3}{4}\right)\pi r^2\)
- Option 4: \(4\pi r^2\) (This matches the standard formula)
Conclusion
The correct formula for the surface area of a sphere is \(4\pi r^2\). Therefore, option 4 is the correct answer.
Important Questions from Solid Figures
A cylindrical tube, open at both ends, is made of a metal sheet which is 0.5 cm thick. Its outer radius is 4 cm and length is 2 m. How much metal (in cm 3) has been used in making the tube?
The volume of a right circular cone is 308 cm 3 and the radius of its base is 7 cm. What is the curved surface area (in cm 2) of the cone? (Take π = \(\frac{22}{7} \) )
The slant height and radius of a right circular cone are in the ratio 29 ∶ 20. If its volume is 4838.4 π cm 3, then its radius is:
Six cubes, each of edge 2 cm, are joined end to end. What is the total surface area of the resulting cuboid in cm 2?
A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:
