NCERT Class 10 Maths — Chapter 12

Exercise 12.1: Surface Area of Combined Solids

Find the surface area when two or more solids are joined — like a cone on top of a cylinder, or a hemisphere on a cone.

combined solidssurface areacone on cylinderhemisphere on cone

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Extra Practice Questions

These questions cover the same concepts as Exercise 12.1. Try solving them to build confidence before or after the textbook exercise.

Water in a canal 6 m wide and 1.5 m deep is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is required? (Use π = 22/7 where necessary)

A.562500 m²

B.500000 m²

C.480000 m²

D.625000 m²

Water flows through a cylindrical pipe of internal diameter 7 cm at the rate of 192.5 litres per minute. In what time (in minutes) will this pipe fill a conical tank whose base radius is 1.4 m and height is 3 m? (Use π = 22/7)

A.25 minutes

B.30 minutes

C.32 minutes

D.35 minutes

A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into cylindrical bottles of diameter 3 cm and height 4 cm. If the liquid fills 'n' bottles completely, and 27π cm³ of liquid remains in the bowl, what is the value of 'n'?

A.45

B.51

C.57

D.63

A solid metallic cylinder is melted and recast into 'n' identical solid cones. If the radius of the cylinder is 3 times the radius of each cone, and the height of the cylinder is 4 times the height of each cone, what is the value of 'n'?

A.72

B.81

C.96

D.108

A solid metallic sphere of radius 'R' is melted and recast into a solid cylinder of radius 'r' and height 'h'. If the radius of the cylinder is also 'R' (i.e., r=R), what is the ratio of the total surface area of the cylinder to the surface area of the sphere?

A.3:2

B.5:3

C.7:6

D.4:3

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. (Use π = 22/7)

A.1.125 m

B.1.5 m

C.1.8 m

D.2.25 m

How many spherical lead shots, each of diameter 4 cm, can be made from a solid rectangular block of lead with dimensions 66 cm × 42 cm × 21 cm? (Use π = 22/7)

A.A) 1730

B.B) 1736

C.C) 1740

D.D) 1742

A solid metallic sphere of radius 3 cm is melted and recast into a solid cylinder of radius 1 cm. What is the height of the cylinder?

A.A) 9 cm

B.B) 18 cm

C.C) 27 cm

D.D) 36 cm

Three metallic spheres of radii 3 cm, 4 cm, and 5 cm, respectively, are melted to form a single solid sphere. By what percentage does the total surface area change (increase or decrease) from the sum of the surface areas of the three small spheres to the surface area of the single large sphere?

A.14% increase

B.20% increase

C.22% decrease

D.28% decrease

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. (Use π = 22/7)

A.1024000 cm³

B.1131428.57 cm³

C.1245000 cm³

D.1357000 cm³

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