CBSE Class 9 Maths Surface Areas and Volumes MCQs Set E

Question: A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diametersof the top and the bottom are 56 cm and 42 cm respectively. How many litres can the bucket hold?
a) 13 L
b) 27 L
c) 42.94 L
d) 28.49 L
Answer: d

Question: To construct a wall 24 m long, 0.4 m thick and 6 m high, bricks of diamensions 25 cm × 16 cm × 10 cm each are used. If the mortar occupies 1/10^th of the volume of the wall, find the number of bricks used.
a) 12960
b) 14420
c) 24566
d) 14296
Answer: a

Question: The ratio between the volume of two sphere is 8 : 27. What is the ratio between their surface areas?
a) 4 : 9
b) 4 : 5
c) 5 : 6
d) 4 : 7
Answer: a

Question: The interior of a building is in the form of cylinder of diameter 4.3 m and height 3.8 m, surmounted by a cone whose vertical angle is a right angle. Find the volume and curved surface area of the building respectively. (Take p = 3.14).
a) 65.56 m³, 71.83 m²
b) 70.24 m³, 62.24 m²
c) 62.26 m³ , 75.56 m²
d) 72.26 m³, 66.46 m²
Answer: a

Question: A cylinder, whose height is two-thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.
a) 4 cm
b) 5 cm
c) 3 cm
d) 6 cm
Answer: a

Question: A sector of a circle of radius 12 cm has the angle 120°. It is rolled up so that two bounding radii are joined together to form a cone. Find the volume of the cone.
a) 189.61 cm³
b) 169.51 cm³
c) 179.61 cm³
d) 125.51 cm³
Answer: a

Question: A tent is made in the form of a frustum of a cone surmounted by another cone. The diameter of the base and the top of the frustum are 20 m and 6 m respectively and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required.
a) 924.71 m²
b) 1402.23 m²
c) 1124.56 m²
d) 1068.57 m²
Answer: d

Question: If the radii of the circular ends of bucket in the form of frustum are 28 cm and 7 cm and the height is 45 cm. The capacity of the bucket is _____.
a) 48150 cm³
b) 48510 cm³
c) 48105 cm³
d) 48205 cm³
Answer: b

Question: A cuboidal metal of dimensions 44 cm × 30 cm × 15 cm was melted and cast into a cylinder of height 28 cm. Its radius is _____.
a) 20 cm
b) 15 cm
c) 10 cm
d) 25 cm
Answer: b

Question: The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?
a) 20 cm
b) 25 cm
c) 10 cm
d) 15 cm
Answer: a

Question: In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person have 4 sq. metres of the space on ground and 20 cubic metres of air to breath. What should be the height of the conical tent?
a) 20 m
b) 15 m
c) 12 m
d) 30 m
Answer: b

Question: A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. The volume of steel used is _____. (Use π = 3.141)
a) 42.15 cm³
b) 41.52 cm³
c) 41.25 cm³
d) 40 cm³
Answer: c

Question: Which of the following statement is INCORRECT?
a) If from a solid cubic block a hemisphere of maximum diameter is cut-off, then surface area of the cubic block is decrease.
b) If two sphere are melted to form a cylinder, then surface area of cylinder is the sum of surface area of twosphere.
c) If a wire is wound about a cylinder so as to cover the whole surface, then length of the wire is equal to the surface area of the cylinder.
d) All of these.
Answer: b

Question: A tent is in the shape of a right circular cylinder up to a height of 3 m and then becomes a right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of ₹ 2 per m², if the radius of the base is 14 m.
a) ₹ 2068
b) ₹ 2156
c) ₹ 2248
d) ₹ 1872
Answer: a

Question: A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8 cm. The diameter of each ball is ____.
a) 0.8 cm
b) 0.4 cm
c) 0.2 cm
d) 0.5 cm
Answer: b

Question: The decorative block shown in the figure i s m a d e o f two solids, a c u b e a n d a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. The total surface area of the block is ____.

a) 150 cm²
b) 160.86 cm²
c) 162.86 cm²
d) 163.86 cm²
Answer: d

Question: A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take p = 22/7)
a) 616 cm³
b) 600 cm³
c) 535 cm³
d) 716 cm³
Answer: a

Question: A conical vessel of radius 12 cm and height 16 cm is completely filled with water. A sphere is lowered into the water and its sized is such that, when it touches the sides, it is just immersed. What fraction of the water overflows ?
a) 3/8
b) 4/7
c) 1/2
d) 59
Answer: a

Question: A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.
a) 6.4 cm
b) 4.2 cm
c) 2.1 cm
d) 5.6 cm
Answer: b

Question: The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is ____.
a) 3
b) 4
c) 5
d) 6
Answer: c

Question: A box opened at the top has its outer dimensions 10 cm × 9 cm × 2.5 cm and its thickness is 0.5 cm, find the volume of the metal.
a) 92.5 cm³
b) 72 cm³
c) 63.5 cm³
d) 81 cm³
Answer: d

Question: The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint 1 cm² of the surface is ₹ 0.05. Find the total cost to painting the vessel all over.
a) ₹ 108.32
b) ₹ 296.28
c) ₹ 101.59
d) ₹ 96.28
Answer: d

Question: Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.
a) 4/3πr²
b) 2πr²
c) 1/3πr²
d) 2/3πr²
Answer: c

Question: An inverted cone of vertical height 12 cm and the radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with the water. [Use π = 22/7]
a) 402.12 cm²
b) 298 cm²
c) 377.14 cm²
d) 315 cm²
Answer: c

Question: Study the question and the statements given below and decide which of the statement(s) is/are necessary to answer the Question: What is the capacity of the cylindrical tank?
I. The area of the base is 61,600 sq. cm.
II. The height of the tank is 1.5 times the radius.
III. The circumference of base is 880 cm.
a) Only I and II
b) Only II and III
c) Only I and III
d) Only II and either I or III
Answer: d