Review each question and reveal answers to strengthen your understanding
1The edge of a cube is 2a cm. Find its surface?
✅ Correct Answer: 4
2The surface of a cube is 24sq cm. Find its volume?
✅ Correct Answer: 1
3The volume of a cube is 1728 cc. Find its surface.
✅ Correct Answer: 1
4How many cubes of edge 2 dm can be cut out of a meter cube?
✅ Correct Answer: 4
5The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
✅ Correct Answer: 4
6The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area?
✅ Correct Answer: 2
7The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
✅ Correct Answer: 1
8The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid.
✅ Correct Answer: 3
9 If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?
✅ Correct Answer: 3
10The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
✅ Correct Answer: 3
11The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
✅ Correct Answer: 2
12Find the length of the wire required to go 15 times round a square field containing 69696 m2.
✅ Correct Answer: 2
13What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
✅ Correct Answer: 4
14The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
✅ Correct Answer: 3
15The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
.
✅ Correct Answer: 3
16If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is?
✅ Correct Answer: 1
17 The spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls. The diameters of two of these are 1 ½ cm and 2 cm respectively. The diameter of third ball is?
✅ Correct Answer: 2
18The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface?
✅ Correct Answer: 3
19The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
✅ Correct Answer: 3
20Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
✅ Correct Answer: 4
21Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder?
✅ Correct Answer: 1
22Find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2.
✅ Correct Answer: 1
23 The radius of the base of cone is 3 cm and height is 4 cm. Find the volume of the cone?
✅ Correct Answer: 1
24The area of a base of a cone is 30 cm2. If the height of the cone is 6cm, find its volume?
✅ Correct Answer: 4
25The area of a base of a cone is 30 cm2. If the height of the cone is 6cm, find its volume?
✅ Correct Answer: 4
26The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
✅ Correct Answer: 3
27Find the ratio between whole surfaces of a sphere and a hemisphere?
✅ Correct Answer: 2
28How many shots of 1cm radius can be prepared from a sphere of 3cm radius?
✅ Correct Answer: 3
29The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
✅ Correct Answer: 2
30Three cubes of metal whose edges are 9, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
✅ Correct Answer: 4
31If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
✅ Correct Answer: 1
32 A rectangular courtyard, the sides of which are in the ratio of 4:3, cost Rs.600 for paving at 50 p per m2; find the length of the diagonal of the courtyard?
✅ Correct Answer: 4
33. How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?
✅ Correct Answer: 4
34A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?
✅ Correct Answer: 2
35The ratio of the volumes of a cube to that of the sphere which will fit inside the cube is?
✅ Correct Answer: 4
36The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm3 of metal used in the box weighs 0.5 gms, the weight of the box is?
✅ Correct Answer: 4
37A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
✅ Correct Answer: 1
38A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 20 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the level of the field will raise by nearly?
✅ Correct Answer: 3
39The area of the cardboard(in cm2) needed to make a box of size 25 cm * 15 cm * 8 cm will be?
✅ Correct Answer: 1
40 The length of the longest rod that can fit in a cubical room of 4 m side is?
✅ Correct Answer: 3
41A cylinder and a cone have a same height and same radius of the base. The ratio between the volumes of the cylinder and cone is?
✅ Correct Answer: 2
42If the height of a cone is increased by 100% then its volume is increased by?
✅ Correct Answer: 1
43In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be?
✅ Correct Answer: 2
44A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
✅ Correct Answer: 4
45If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
✅ Correct Answer: 2
46Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
✅ Correct Answer: 3
47A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
✅ Correct Answer: 2
48The sides of a cube are in the ratio 1:2 the ratio of their volume is?
✅ Correct Answer: 3
49 The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?
✅ Correct Answer: 2
50Surface area of two spheres are in the ratio 1:4 what is the ratio of their volumes?
✅ Correct Answer: 2
51The height of two right circular cones are in the ratio 1:2 and their perimeters of their bases are in the ratio 3:4, the ratio of their volume is?
✅ Correct Answer: 3
52The surface area of a cube is 726m2, its volume is?
✅ Correct Answer: 2
53 If the length, breadth and the height of a cuboid are in the ratio 6: 5: 4 and if the total surface area is 33300 cm2, then length breadth and height in cms, are respectively?
✅ Correct Answer: 4
54A wooden box of dimensions 8m x 7m x 6m is to carry rectangular boxes of dimensions 8cm x 7cm x 6cm. The maximum number of boxes that can be carried in 1 wooden box is?
✅ Correct Answer: 2
55A metal sheet 27 cm long 8cm broad and 1 cm thick is melted into a cube. The difference between the surface areas of two solids is
✅ Correct Answer: 2
56 If the volumes of two cubes are in the ratio 8: 1, the ratio of their edges is
✅ Correct Answer: 3
57The radius of a wire is decreased to one “third if volume remains the same length will increase
✅ Correct Answer: 4
58 The length of the wire of 0.2mm radius that can be drawn after melting a solid copper sphere of diameter 18cm?
✅ Correct Answer: 4
59The 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?
✅ Correct Answer: 3
60 The radius of a circular cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is?
✅ Correct Answer: 1
61A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is
✅ Correct Answer: 4
62The radii of two spheres are in the ratio 1: 2. The ratio of their surface areas is?
✅ Correct Answer: 2
63 If the volume and surface area of a sphere is numerically the same then it's radius is
✅ Correct Answer: 3
64 If the volume and surface area of a sphere is numerically the same then it's radius is
✅ Correct Answer: 3
65The radii of two cylinders are in the ratio of 2: 3 and their heights are in the ratio 5: 3. The ratio of their volumes is:
✅ Correct Answer: 2
66A cylindrical piece of metal of radius 2 cm and height 6cm is shaped into a cone of the same radius. The height of the cone is:
✅ Correct Answer: 1
67If a right circular cone of vertical height 24 cm has a volume of 132 cm3, then the area of its curved surface is:
✅ Correct Answer: 3
68 If the volumes of two cones are in the ratio 1: 4 and their diameters are in the ratio 4: 5, then the ratio of their heights is?
✅ Correct Answer: 4
69A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone then the height of the cylinder is?
✅ Correct Answer: 3
70 If the radius of the sphere is doubled then it's volume is increased by?
✅ Correct Answer: 3
71The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
✅ Correct Answer: 2
72A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
✅ Correct Answer: 2
73 What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
✅ Correct Answer: 3
74A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
✅ Correct Answer: 3
75 Surface area of a sphere is 2464 cm2. If its radius is doubled, then the surface area of the new sphere will be