CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set 06

Case Based MCQs

Case I : Read the following passage and answer the questions.

Science Project

Arun a 10th standard student makes a project on corona virus in science for an exhibition in his school. In this project, he picks a sphere which has volume 38808 cm³ and 11 cylindrical shapes, each of volume 1540 cm³ with length 10 cm.

Question. Diameter of the base of the cylinder is
(a) 7 cm
(b) 14 cm
(c) 12 cm
(d) 16 cm

Answer: B

Question. Diameter of the sphere is
(a) 40 cm
(b) 42 cm
(c) 21 cm
(d) 20 cm

Answer: B

Question. Total volume of the shape formed is
(a) 85541 cm³
(b) 45738 cm³
(c) 24625 cm³
(d) 55748 cm³

Answer: D

Question. Curved surface area of the one cylindrical shape is
(a) 850 cm²
(b) 221 cm²
(c) 440 cm²
(d) 540 cm²

Answer: C

Question. Total area covered by cylindrical shapes on the surface of sphere is
(a) 1694 cm²
(b) 1580 cm²
(c) 1896 cm²
(d) 1470 cm²

Answer: A

Case II : Read the following passage and answer the questions.

Visit to Sanchi Stupa

Ajay is a Class X student. His class teacher Mrs. Kiran arranged a historical trip to great Stupa of Sanchi. She explained that Stupa of Sanchi is great example of architecture in India. Its base part is cylindrical in shape. The dome of this stupa is hemispherical in shape, known as Anda. It also contains a cubical shape part called Hermika at the top. Path around Anda is known as Pradakshina Path.

Question. Find the lateral surface area of the Hermika, if the side of cubical part is 8 m.
(a) 128 m²
(b) 256 m²
(c) 512 m²
(d) 1024 m²

Answer: B

Question. The diameter and height of the cylindrical base part are respectively 42 m and 12 m. If the volume of each brick used is 0.01 m³, then find the number of bricks used to make the cylindrical base.
(a) 1663200
(b) 1580500
(c) 1765000
(d) 1865000

Answer: A

Question. If the diameter of the Anda is 42 m, then the volume of the Anda is
(a) 17475 m³
(b) 18605 m³
(c) 19404 m³
(d) 18650 m³

Answer: C

Question. The radius of the Pradakshina path is 25 m. If Buddhist priest walks 14 rounds on this path, then find the distance covered by the priest.
(a) 1860 m
(b) 3600 m
(c) 2400 m
(d) 2200 m

Answer: D

Question. The curved surface area of the Anda is
(a) 2856 m²
(b) 2772 m²
(c) 2473 m²
(d) 2652 m²

Answer: B

Case III : Read the following passage and answer the questions.

Classroom Activity

To make the learning process more interesting, creative and innovative, Amayra’s class teacher brings clay in the classroom, to teach the topic - Surface Areas and Volumes. With clay, she forms a cylinder of radius 6 cm and height 8 cm. Then she moulds the cylinder into a sphere and asks some questions 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) 528 cm²
(b) 756 cm²
(c) 625 cm²
(d) 636 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

Assertion & Reasoning Based MCQs

Directions In these questions, a statement of Assertion is followed by a statement of Reason is given. Choose
the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : The sum of the length, breadth and height of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area is 236 cm².
Reason : The lateral surface area of a cuboid is 2(l + b).

Answer: C

Question. Assertion : If the areas of three adjacent faces of a cuboid are x, y, z respectively then the volume of the cuboid is √xyz.
Reason : Volume of a cuboid whose edges are l, b and h is lbh units.

Answer: A

Question. Assertion : The volume of a hall, which is 5 times as high as it is broad and 8 times as long as it is high, is 12.8 m3. The breadth of the hall is 25 cm.
Reason : The total surface area of a cuboid of length (l), breadth (b) and height (h) is 2[lb + bh + lh].

Answer: D

Question. Assertion : From a solid cylinder, whose height is 12 cm and diameter 10 cm a conical cavity of same height and same diameter is hollowed out. Then,volume of the cone is (2200/7)cm³.
Reason : If a conical cavity of same height and same diameter is hollowed out from a cylinder of height h and base radius r, then volume of the cone will be half of the volume of the cylinder.

Answer: C

Question. Assertion : A godown building is in the form as shown in the figure. The vertical cross section parallel to the width side of the building is a rectangle 7 m × 3 m, mounted by a semicircle of radius 3.5 m. The inner measurements of the cuboidal portion of the building are 10 m × 7 m × 3 m. Then, the volume of the godown is 406 m3.
Reason : Volume of the solid made up by combination of two or more basic solids will be equal to the sum of the volumes of the constituent basic solid.

Answer: D

Question. Assertion : A well of diameter 4 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it to a width of 2 m to form an embankment. Then the height of the embankment is 4(2/3)m.
Reason : Volume of cylinder = pr²h, where h is height and r is the radius of the cylinder.

Answer: A

Question. Assertion : The curved surface area of a cone of base radius 6 cm and height 8 cm is 60p cm².
Reason : Curved surface area of a cone = pr2h, where r be the radius and h be the height of cone.

Answer: C

Question. Assertion : The slant height of the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Then, the curved surface area of the frustum is 48 cm².
Reason : If the radii of the circular ends of the frustum of a cone are r1 and r2 respectively and its height is h, then its curved surface area is p(r₁ + r₂)l, where l² = h² – (r¹ + r²)².

Answer: C