Math՚s: Meaning of Surface Area and Volume: Surface Area, Volume of Sphere and Hemisphere (For CBSE, ICSE, IAS, NET, NRA 2022)

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Sphere

The locus of a point which moves in space in such a way that its distance from a fixed point remains the same is called a sphere. The fixed point is called the center of the sphere and the same distance is called the radius () of the sphere. Examples of sphere are football, cricket ball, a marble etc.

Surface Area: Sphere

Volume of Sphere-

Surface Area of Sphere-

Hemisphere

If a sphere is cut into two equal parts by a plane passing through its center, then each part is called a hemisphere.

Surface Area: Hemisphere
  • Volume of Hemisphere-
  • Curved Surface Area of Hemisphere-
  • Total Surface Area of Hemisphere-

1. Diameter of a hemispherical toy is . Find its

(i) curved surface area

(ii) total surface area

(iii) volume

Solution- Given, then,

(i)

(ii)

(iii)

2. A metallic solid ball of radius is melted and converted into small solid balls of radius each. Find the number of small balls so formed.

Solution-

The number of small balls formed from the big ball is .

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