Surface Areas And Volumes Class 10 Extra Questions

CHAPTER – 12         (SURFACE AREAS AND VOLUMES)                   CLASS – X 

MULTIPLE CHOICE QUESTIONS (Surface Areas And Volumes Class 10 Extra Questions)

1. What is the total surface area of a solid hemisphere of diameter d?
   a)3πd²                  b) 2πd²              c)   ½πd²              d) ¾ πd²
2. The radius ( in cm ) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is___

a)  4.2                              b) 2.1                       c) 8.4                          d) 1.05
3. A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is____
a) 1:3                               b) 1:2                        c) 2:1                          d) 3: 1
4. A solid is hemispherical at bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and height of its conical part, is :
a) 1 : √3                         b) 2 : √3                  c) √3 : 2                     d) 1 : 2
5.  The total surface area of a solid hemisphere of radius 7 cm is ____cm²
a) 447

                            b) 239                     c) 147                       d) 174    

            
6. A spherical iron ball is dropped into a cylindrical vessel of base diameter 14 cm, containing water. The water level is increased by 9  cm. The radius of the ball is
a)3.5 cm                         b) 7 cm                      c) 9cm                        d) 12 cm
7. Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 min?
a)  800 m³                                   b) 4000 m³                c) 8000 m³                  d) 2000 m³

SUBJECTIVE TYPE QUESTIONS (Surface Areas And Volumes Class 10 Extra Questions)

8. Two cones have their heights in the ratio 1:3 and radii in the ratio 3:1, what is the ratio of their volumes?
9. A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166cm³. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs10 per cm².
10. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36cm partly filled with water. If the sphere is completely submerged, then find the height of the water level rises.
11. A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of 3/2 cm and its depth 8/9 cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
12. The rain water from 22m x 20m roof drains into a cylindrical vessel of diameter 2m and height 3.5 m. If the rain water collected from the roof fills (4/5)th of cylindrical vessel then find the rainfall in cm. 

13.  A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
14. A circus tent is in the shape of a cylinder surmounted by a conical roof. If the common diameter is 56 m, the height of the cylindrical portion is 6 m and height of the roof from the ground is 27 m, then find the area of the canvas used for the tent.
15.  An iron pillar consists of a cylindrical portion 240 cm high and 16 cm in diameter and a cone 36cm high surmounting it. Find the weight of the pillar if 1  cu.cm of iron weighs 7.8g.
16. What is the ratio of volume of a cube to that of a sphere which will fit inside it ?
17. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid is 1628 sq.cm. find the volume of cylinder.( use  = 22/7)
18.  A toy is in the form of a hemisphere surmounted by a right circular cone of the same radius as that of the hemisphere. If the radius of the cone is 21 cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and surface area of the toy.
19. A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 4 cm and the diameter of the base is 8 cm. If a right circular cylinder circumscribes the solid. Find, how much space is left to cover?
20. Assertion: Number of spherical balls that can be made out of a solid cube lead whose edge is 44cm each ball being 4 cm in diameter are 2541

Reason: Number of balls = ( volume of one ball )/( volume of lead)
21. Assertion: If volumes of two spheres are in the ratio 64 : 27, then the ratio of their surface area, is 4 : 3
Reason: Volume of a right circular cylinder is r²h.

• CASE STUDY

A golf ball is spherical with about 300-500  dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a Golf ball has diameter 4.2 cm and surface has 315 dimples (hemispherical) of radius 2 mm.

 Based on the above information answer the following questions
1. Find the surface area of one such simple
2. Find the volume of the material dug out to make one dimple.
3. Find the total surface area exposed to the surroundings
4. Find the volume of the Gulf ball

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