CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set D

Case Based MCQs

Case I : Read the following passage and answer the questions.
Science Project
Arun a \( 10^{th} \) 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 \( 38808 \text{ cm}^3 \) and 11 cylindrical shapes, each of volume \( 1540 \text{ cm}^3 \) 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) \( 85541 \text{ cm}^3 \)
(b) \( 45738 \text{ cm}^3 \)
(c) \( 24625 \text{ cm}^3 \)
(d) \( 55748 \text{ cm}^3 \)
Answer: (d)

Question. Curved surface area of the one cylindrical shape is
(a) \( 850 \text{ cm}^2 \)
(b) \( 221 \text{ cm}^2 \)
(c) \( 440 \text{ cm}^2 \)
(d) \( 540 \text{ cm}^2 \)
Answer: (c)

Question. Total area covered by cylindrical shapes on the surface of sphere is
(a) \( 1694 \text{ cm}^2 \)
(b) \( 1580 \text{ cm}^2 \)
(c) \( 1896 \text{ cm}^2 \)
(d) \( 1470 \text{ cm}^2 \)
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) \( 128 \text{ m}^2 \)
(b) \( 256 \text{ m}^2 \)
(c) \( 512 \text{ m}^2 \)
(d) \( 1024 \text{ m}^2 \)
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 \( 0.01 \text{ m}^3 \), 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) \( 17475 \text{ m}^3 \)
(b) \( 18605 \text{ m}^3 \)
(c) \( 19404 \text{ m}^3 \)
(d) \( 18650 \text{ m}^3 \)
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) \( 2856 \text{ m}^2 \)
(b) \( 2772 \text{ m}^2 \)
(c) \( 2473 \text{ m}^2 \)
(d) \( 2652 \text{ m}^2 \)
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) \( 905.14 \text{ cm}^3 \)
(b) \( 903.27 \text{ cm}^3 \)
(c) \( 1296.5 \text{ cm}^3 \)
(d) \( 1156.63 \text{ cm}^3 \)
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) \( 528 \text{ cm}^2 \)
(b) \( 756 \text{ cm}^2 \)
(c) \( 625 \text{ cm}^2 \)
(d) \( 636 \text{ cm}^2 \)
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)

Assertion & Reasoning Based MCQs

Question. Assertion : The sum of the length, breadth and height of a cuboid is 19 cm and its diagonal is \( 5\sqrt{5} \) cm. Its surface area is \( 236 \text{ cm}^2 \).
Reason : The lateral surface area of a cuboid is \( 2(l + b) \).
(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.
Answer: (b)

Question. Assertion : If the areas of three adjacent faces of a cuboid are x, y, z respectively then the volume of the cuboid is \( \sqrt{xyz} \).
Reason : Volume of a cuboid whose edges are l, b and h is lbh units.
(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.
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 \( 12.8 \text{ m}^3 \). 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 \( 2[lb + bh + lh] \).
(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.
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 \( \frac{2200}{7} \text{ cm}^3 \).
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.
(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.
Answer: (c)

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 \( 4 \frac{2}{3} \text{ m} \).
Reason : Volume of cylinder = \( \pi r^2 h \), where h is height and r is the radius of the cylinder.
(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.
Answer: (b)

Question. Assertion : The curved surface area of a cone of base radius 6 cm and height 8 cm is \( 60\pi \text{ cm}^2 \).
Reason : Curved surface area of a cone = \( \pi r^2 h \), where r be the radius and h be the height of cone.
(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.
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 \( 48 \text{ cm}^2 \).
Reason : If the radii of the circular ends of the frustum of a cone are \( r_1 \) and \( r_2 \) respectively and its height is h, then its curved surface area is \( \pi(r_1 + r_2)l \), where \( l^2 = h^2 - (r_1 + r_2)^2 \).
(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.
Answer: (c)

Very Short Answer Type Questions 

Question. Find the radius of a sphere (in cm) whose volume is \( 12\pi \text{ cm}^3 \).
Answer: Radius \( r = \sqrt[3]{9} \text{ cm} \).

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.
Answer: The ratio is 1 : 4.

Question. A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then what will be the ratio of its radius and the slant height of the conical part?
Answer: Ratio of radius to slant height \( r : l = 1 : 2 \).

Question. Find the number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm.
Answer: 5 solid spheres.

Question. A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part is half the conical part, then find the ratio of the radius and the height of the conical part.
Answer: Ratio \( r : h = 1 : \sqrt{15} \).

Question. A cuboidal solid block of metal 49 cm × 44 cm × 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
Answer: Radius \( r = 21 \text{ cm} \).

Question. 2 cubes, each of volume \( 125 \text{ cm}^3 \), are joined end to end. Find the surface area of the resulting cuboid.
Answer: Surface area = \( 250 \text{ cm}^2 \).

Question. Find the total surface area of solid opened at the top in the given figure.
Answer: Total Surface Area = \( 2\pi rh + 2\pi r^2 \) (area of cylindrical wall + area of hemispherical base).

Question. The total surface area of a cube is \( 32 \frac{2}{3} \text{ m}^2 \). Find the volume of cube.
Answer: Volume = \( \frac{343}{27} \text{ m}^3 \) or \( 12 \frac{19}{27} \text{ m}^3 \).

Question. If curved surface area of cylinder is equal to its volume. What is the radius of cylinder?
Answer: Radius \( r = 2 \text{ units} \).

Short Answer Type Questions 

Question. How many cubes of side 2 cm can be made from a solid cube of side 10 cm?
Answer: 125 cubes.

Question. A cone and a cylinder have the same radii but the height of the cone is 3 times that of the cylinder. Find the ratio of their volumes.
Answer: The ratio of volume of cone to cylinder is 1 : 1.

Question. If the total surface area of a solid hemisphere is \( 462 \text{ cm}^2 \), find its volume. [Take \( \pi = \frac{22}{7} \)]
Answer: Volume = \( 718.67 \text{ cm}^3 \) (or \( \frac{2156}{3} \text{ cm}^3 \)).

Question. The volume of a hemisphere is \( 2425 \frac{1}{2} \text{ cm}^3 \). Find its curved surface area. [Use \( \pi = \frac{22}{7} \)]
Answer: Curved Surface Area = \( 693 \text{ cm}^2 \).