CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set 03

Question. A cylindrical pencil sharpened at one edge is the combination of
(a) a cone and a cylinder
(b) cube and a cylinder
(c) a hemisphere and a cylinder
(d) two cylinders
Answer : A

Question. A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is
(a) (1/6)πa³
(b) (4/3)πa³
(c) (1/3)πa³
(d) None of these
Answer : A

Question. A cubical icecreambrick of edge 22 cmis to be distributed among some children by filling icecream cones of radius 2 cm and height 7 cm upto its brim. How many children will get icecream cones?
(a) 163
(b) 263
(c) 363
(d) 463
Answer : C

Question. The shape of a gilli, in the gilli-danda game (see figure) is a combination of

(a) two cylinders
(b) a cone and a cylinder
(c) two cones and a cylinder
(d) two cylinders and a cone
Answer : C

Question. If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is
(a) 4πr²
(b) 6πr²
(c) 3πr²
(d) 8πr²
Answer : A

Question. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius.
The total surface area of the shape so formed is
(a) 4πr(h² + r²)
(b) 4πr[h + r]
(c) 4π(h² + r²)
(d) None of the above
Answer : D

Question. The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is πr²/2 [3h − 2r].

Answer : C

Question. A surahi is the combination of
(a) a sphere and a cylinder
(b) a hemisphere and a cylinder
(c) two hemispheres
(d) a cylinder and a cone
Answer : A

 

Question. Three cubes each of side 5 cm are joined end to end, then the surface area of the resulting solid is
(a) 250 cm²
(b) 180 cm²
(c) 350 cm²
(d) None of these
Answer : C

Question. A right circular cylinder of radius r cm and height h cm(where, h > 2r) just encloses a sphere of diameter
(a) r cm
(b) 2r cm
(c) h cm
(d) 2h cm
Answer : B

Question. Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3: 1, then the ratio of their volumes is
(a) 1 : 3
(b) 3 : 1
(c) 2 : 3
(d) 3 : 2
Answer : B

Question. From a solid circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed, then the volume of remaining solid is
(a) 280 π cm³
(b) 330 π cm³
(c) 240 π cm³
(d) 440 π cm³
Answer : C

Question. A plumbline (sahul) is the combination of (see figure)

(a) a cone and a cylinder
(b) a hemisphere and a cone
(c) cube and a cylinder
(d) sphere and cylinder
Answer : B

Question. A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is
(a) πrl + 2πrh
(b) πr² (1 + 2h)
(c) πr[√r² + h² + 2h + r]
(d) None of these
Answer : C

Question. Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. The water level rises by 5.6 cm. When marble dropped into the beaker, then the number of marble is
(a) 150
(b) 160
(c) 175
(d) 235
Answer : A

Question. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm.
The length of the wire is
(a) 12 m
(b) 18 m
(c) 36 m
(d) 66 m
Answer : C

Question. During conversion of a solid from one shape to another, the volume of the new shape will
(a) increase
(b) decrease
(c) remain unaltered
(d) be doubled
Answer : C

Question. A heap of rice is in the formof a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas as cloth is required to just cover the heap? 
(a) 105.5 m²
(b) 471.42 m²
(c) 173.5 m²
(d) None of these
Answer : B

Question. A 20 m deep well, with diameter 7 m is dug and the earth from digging is evently spread out to form a platform 22 m by 14 m. The height of the platform is 
(a) 2.5 m
(b) 3.5 m
(c) 3 m
(d) 2 m
Answer : A

Question. If the radius of the base of a right circular cylinder is halved, keeping the height same, then find the ratio of the volume of the cylinder thus obtained to the volume of original cylinder. 
(a) 1/3
(b) 1/4
(c) 1/2
(d) 1/5
Answer : B

Question. A mason constructs a wall of dimensions 270 cm× 300 cm× 350 cmwith the bricks each of size 22.5 cm × 11.25 cm× 8.75 cmand it is assumed that 1/8 space is covered by the mortar. Then, the number of bricks used to construct the wall is
(a) 11100
(b) 11200
(c) 11000
(d) 11300
Answer : B

Question. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article.

(a) 374 cm²
(b) 370 cm²
(c) 475 cm²
(d) None of these
Answer : A

Case Based MCQs

A. To make the learning process more interesting creative and innovative Shavya’s class teacher brings clay in the classroom, to teach the topic. Surface Areas and Volumes. With clay, she forms a cylinder of radius 4 cm and height 18 cm. Then, she moulds the cylinder into a sphere and ask some question to students.

Question. The radius of the sphere so formed is
(a) 4 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Answer : B

Question. The volume of the sphere so formed is
(a) 905.14 cm³
(b) 903.27 cm³
(c) 1296.5 cm³
(d) 1156.63 cm³
Answer : A

Question. Find the ratio of the volume of sphere to the volume of cylinder.
(a) 2 : 1
(b) 1 : 2
(c) 1 : 1
(d) 3 : 1
Answer : C

Question. Total surface area of the cylinder is
(a) 553.14 cm²
(b) 751.52 cm²
(c) 625 cm²
(d) 785.38 cm²
Answer : A

Question. During the conversion of a solid from one shape to another the volume of new shape will
(a) be increase
(b) be decrease
(c) remain unaltered
(d) be double
Answer : C

B. Geeta and Meena have 10 and 6 CD respectively, each of radius 4 cm and thickness 1 cm. They place their CD one above the other to form solid cylinders.

Based on the above information, answer the following questions.

Question. Curved surface area of the cylinder made by Geeta is
(a) 308.17 cm²
(b) 132 cm²
(c) 154 cm²
(d) 251.42 cm²
Answer : D

Question. The ratio of curved surface area of the cylinder made by Geeta and Meena is
(a) 3 : 5
(b) 3 : 2
(c) 5 : 3
(d) 5 : 7
Answer : C

Question. The volume of the cylinder made by Meena is
(a) 301.44 cm³
(b) 144 cm³
(c) 132 cm³
(d) 208.42 cm³
Answer : A

Question. The ratio of the volume of the cylinders made by Geeta and Meena is
(a) 1 : 2
(b) 2 : 5
(c) 3 : 5
(d) 5 : 3
Answer : D

Question. When two CD Cassette are shifted from Geeta cylinder to Meena’s cylinder, then
(a) Volume of two cylinder become equal
(b) Volume of Geeta’s cylinder > Volume of Meena’s cylinder
(c) Volume of Meena’s cylinder > Volume of Geeta’s cylinder
(d) None of the above
Answer : A

C. The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of
Indian Architecture. It was originally commissioned by the emperor Ashoka in the 3rd century BCE. Its nucleus was a simple hemispherical brick structure built over the relics of the Buddha. It is a perfect example of combination of solid figures. A big hemispherical dome with a cuboidal structure mounted on it.
(take π = 22/7)

Question. The cloth require to cover the hemispherical dome if the radius of its base is 14m is
(a) 1222 sq m
(b) 1232 sq m
(c) 1200 sq m
(d) 1400 sq m
Answer : B

Question. The total surface area of the combined figure i.e. hemispherical dome with radius 14 m and cuboidal shaped top with dimensions 8 m × 6 m × 4 m is
(a)1200 sq m
(b) 1232 sq m
(c) 1392 sq m
(d) 1932 sq m
Answer : C

Question. Calculate the volume of the hemispherical dome if the height of the dome is 21 m.
(a) 19404 cu m
(b) 2000 cu m
(c) 15000 cu m
(d) 19000 cu m
Answer : A

Question. The formula to find the volume of sphere is
(a) (2/3)πr³
(b) (4/3)πr³
(c) 4πr²
(d) 2πr²
Answer : B

Question. The volume of the cuboidal shaped top is with dimensions mentioned in question (iv).
(a) 182.45 m³
(b) 282.45 m³
(c) 292 m³
(d) 192
Answer : D

 

 

 

 

 

 

 

 

Please click on below link to download CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set C