NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes

Exercise 12.1

A cylindrical pencil sharpened at one edge is the combination of

A surahi is the combination of

A plumbline (sahul) is the combination of (see Fig.)

The shape of a glass (tumbler) (see Fig.) is usually in the form of

The shape of a gilli, in the gilli–danda game (see Fig.), is a combination of

A shuttlecock used for badminton has the shape of the combination of

A cone is cut by a plane parallel to its base and the cone on one side of the plane is removed. The part left is called

A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm. If \(\dfrac{1}{8}\) of the space remains unfilled, then the number of marbles the cube can accommodate is

A metallic spherical shell with internal and external diameters 4 cm and 8 cm is recast into a cone of base diameter 8 cm. The height of the cone is

A solid iron cuboid of dimensions 49 cm \(\times\) 33 cm \(\times\) 24 cm is moulded into a sphere. The radius of the sphere is

A wall of dimensions 270 cm \(\times\) 300 cm \(\times\) 350 cm is built with bricks of size 22.5 cm \(\times\) 11.25 cm \(\times\) 8.75 cm. If \(\dfrac{1}{8}\) of the space is covered by mortar, the number of bricks used is

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

The radii of the top and bottom of a bucket (frustum) are 28 cm and 7 cm, and its slant height is 45 cm. The curved surface area is

A medicine capsule is a cylinder of diameter 0.5 cm with two hemispherical ends. The length of the capsule is 2 cm. Its capacity is

Two solid hemispheres of the same base radius \(r\) are joined along their bases. The curved surface area of the new solid is

A right circular cylinder of radius \(r\) cm and height \(h\) cm (with \(h>2r\)) just encloses a sphere. The diameter of the sphere is

During conversion of a solid from one shape to another, the volume of the new shape will

The diameters of the two circular ends of a bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is (in litres)

In a right circular cone, the cross-section made by a plane parallel to the base is a

Volumes of two spheres are in the ratio \(64:27\). The ratio of their surface areas is