CBSE Class 10 Maths HOTs Surface Area and Volumes Set C

Multiple Choice Questions

Question. Three cubes each of side 5 cm are joined end to end, then the surface area of the resulting solid is
(a) 250 cm\(^2\)
(b) 180 cm\(^2\)
(c) 350 cm\(^2\)
(d) None of these
Answer: (c)

Question. A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is
(a) \( \frac{1}{6} \pi a^3 \)
(b) \( \frac{4}{3} \pi a^3 \)
(c) \( \frac{1}{3} \pi a^3 \)
(d) None of these
Answer: (a)

Question. A cubical icecream brick of edge 22 cm is 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. 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. 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) \( 4\pi r^2 \)
(b) \( 6\pi r^2 \)
(c) \( 3\pi r^2 \)
(d) \( 8\pi r^2 \)
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) \( 4\pi r(h^2 + r^2) \)
(b) \( 4\pi r[h + r] \)
(c) \( 4\pi (h^2 + r^2) \)
(d) None of the above
Answer: (b)

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 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. 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. 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) \( \pi rl + 2\pi rh \)
(b) \( \pi r^2(l + 2h) \)
(c) \( \pi r[\sqrt{r^2 + h^2} + 2h + r] \)
(d) None of these
Answer: (c)

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. 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 radius is removed, then the volume of remaining solid is
(a) \( 280 \pi \text{ cm}^3 \)
(b) \( 330 \pi \text{ cm}^3 \)
(c) \( 240 \pi \text{ cm}^3 \)
(d) \( 440 \pi \text{ cm}^3 \)
Answer: (c)

Question. A 20 m deep well, with diameter 7 m is dug and the earth from digging is evenly 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) \( \frac{1}{3} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{5} \)
Answer: (b)

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. A heap of rice is in the form of 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 m\(^2\)
(b) 471.42 m\(^2\)
(c) 173.5 m\(^2\)
(d) None of these
Answer: (b)

Question. A mason constructs a wall of dimensions 270 cm \(\times\) 300 cm \(\times\) 350 cm with the bricks each of size 22.5 cm \(\times\) 11.25 cm \(\times\) 8.75 cm and it is assumed that \( \frac{1}{8} \) 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)

Case Based MCQs

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 cm\(^3\)
(b) 903.27 cm\(^3\)
(c) 1296.5 cm\(^3\)
(d) 1156.63 cm\(^3\)
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 cm\(^2\)
(b) 751.52 cm\(^2\)
(c) 625 cm\(^2\)
(d) 785.38 cm\(^2\)
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)

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 cm\(^2\)
(b) 132 cm\(^2\)
(c) 154 cm\(^2\)
(d) 251.42 cm\(^2\)
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 cm\(^3\)
(b) 144 cm\(^3\)
(c) 132 cm\(^3\)
(d) 208.42 cm\(^3\)
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)

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 \( \pi = \frac{22}{7} \))

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) \( \frac{2}{3} \pi r^3 \)
(b) \( \frac{4}{3} \pi r^3 \)
(c) \( 4\pi r^2 \)
(d) \( 2\pi r^2 \)
Answer: (b)

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 \(\times\) 6 m \(\times\) 4 m is
(a) 1200 sq m
(b) 1232 sq m
(c) 1392 sq m
(d) 1932 sq m
Answer: (c)

Question. The volume of the cuboidal shaped top is with dimensions mentioned in question (iv).
(a) 182.45 m\(^3\)
(b) 282.45 m\(^3\)
(c) 292 m\(^3\)
(d) 192 m\(^3\)
Answer: (d)

Multiple Choice Questions

Question. How many cubes of side \( 2 \text{ cm} \) can be made from a solid cube of side \( 10 \text{ cm} \)?
(a) 100
(b) 125
(c) 175
(d) 200
Answer: (b)

Question. 2 cubes, each of volume \( 125 \text{ cm}^3 \), are joined end to end. Find the surface area of the resulting cuboid.
(a) \( 100 \text{ cm}^2 \)
(b) \( 200 \text{ cm}^2 \)
(c) \( 225 \text{ cm}^2 \)
(d) \( 250 \text{ cm}^2 \)
Answer: (d)

Question. The radius of a sphere (in cm) whose volume is \( 12\pi \text{ cm}^3 \), is
(a) 3
(b) \( 3\sqrt{3} \)
(c) \( 3^{2/3} \)
(d) \( 3^{1/3} \)
Answer: (c)

Question. A solid spherical ball fits exactly inside the cubical box of side \( 2a \). The volume of the ball is
(a) \( \frac{16}{3} \pi a^3 \)
(b) \( \frac{1}{6} \pi a^3 \)
(c) \( \frac{32}{3} \pi a^3 \)
(d) \( \frac{4}{3} \pi a^3 \)
Answer: (d)

Question. A cone and a cylinder have the same radii but the height of the cone is 3 times that of the cylinder, then the ratio of their volumes.
(a) 1 : 2
(b) 2 : 1
(c) 1 : 1
(d) None of these
Answer: (c)

Short Answer Type Questions

Question. A hemispherical depression is cut out from one face of a cuboidal block of side \( 7 \text{ cm} \) such that the diameter of the hemisphere is equal to the edge of the cube. Find the surface area of the remaining solid.
Answer: \( 332.465 \text{ cm}^2 \)

Question. The capacity of a cylindrical glass tumbler is \( 125.6 \text{ cm}^3 \). If the radius of the glass tumbler is \( 2 \text{ cm} \), then find its height. (Use \( \pi = 3.14 \))
Answer: \( 10 \text{ cm} \)

Long Answer Type Questions

Question. From a solid cylinder whose height is \( 2.4 \text{ cm} \) and diameter \( 1.4 \text{ cm} \), a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest \( \text{cm}^2 \).
Answer: \( 18 \text{ cm}^2 \)

Question. A well of diameter \( 3 \text{ m} \) is dug \( 14 \text{ m} \) deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width \( 4 \text{ m} \) to form a platform. Find the height of the platform. [take \( \pi = \frac{22}{7} \)]
Answer: \( 1.125 \text{ m} \)