Which of the following represents the total surface area of a sphere?
\(4\pi r^2\)
The total surface area of a solid is the whole area of the surface that encloses it.
A sphere is bounded by a single continuous curved surface with no flat faces and no edges, so its total surface area is simply that one curved area.
The standard geometric result for a sphere of radius r is total surface area \(=4\pi r^2\).
A useful way to remember it is that the sphere's surface equals four times the area of its great circle, \(\pi r^2\).
The option \(2\pi r^2\) is the curved surface of a hemisphere, so it is only half the sphere's area.
The option \(\pi r^2\) is the area of a flat circle of radius r, not a three-dimensional surface, and \(3\pi r^2\) has no standard meaning for a sphere.
Hence, the answer is \(4\pi r^2\).
Similar Questions
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
Which of the following is a geometrical figure with a three-dimensional geometry that has eight vertices and six rectangular faces?
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- If two hemispheres of curved surface area \(8\pi \text{ cm}^2\) each are joined together to form a sphere. What is the volume of the sphere so formed in \(\text{cm}^3\)?
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Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
Which of the following is a geometrical figure with a three-dimensional geometry that has eight vertices and six rectangular faces?
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$
