Q1:
2026: 6 June Shift 1
Geometry
Solids
Medium
Three solid cubes of sides 1 cm, 6 cm, and 8 cm are melted to form a new cube. The surface area of the cube so formed is:
2026: 6 June Shift 1
Geometry
Solids
Medium
Three solid cubes of sides 1 cm, 6 cm, and 8 cm are melted to form a new cube. The surface area of the cube so formed is:
2026: 31 May Shift 2
Geometry
Solids
Easy
Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. The surface area of new cube is:
2026: 31 May Shift 2
Geometry
Solids
Medium
A rectangular block with sides 6 cm, 12 cm and 15 cm is cut up into an exact number of equal cubes. The least possible number of cubes is?
2026: 31 May Shift 1
Geometry
Solids
Medium
Arrange the volumes of the following geometrical figures in decreasing order of their value.
A. A cuboid of length 5 cm, breadth 3 cm and height 4 cm.
B. A cube on each side of 4 cm.
C. A cylinder of radius 3 cm and length 3 cm.
D. A sphere of radius 3 cm.
Choose the correct answer from the options given below:
2026: 30 May Shift 2
Geometry
Solids
Medium
Consider the surface area of the following solids.
(A) A cylinder with a diameter of base 14 cm and height 80 cm.
(B) A cone with a radius of 7 cm and slant height 10 cm.
(C) A sphere with a radius 7 cm.
(D) A hemisphere with a radius of 21 cm.
Arrange the above in decreasing order.
Choose the correct answer from the options given below:
2026: 30 May Shift 1
Geometry
Solids
Hard
A hemispherical bowl is 176 cm round the brim. Supposing it to be half full, how many peoples may be served from it in hemispherical glasses 4 cm in diameter at the top?
2026: 29 May Shift 2
Geometry
Solids
Medium
Find the total surface area of a solid hemisphere of diameter 14 cm.
2026: 29 May Shift 1
Geometry
Solids
Medium
The solid and the Surface area (S.A) of the following solids are given below.
(A) A cube of edge 9 cm., S.A =
(B) A cuboid of 18 cm. long, 14 cm. width and 7 cm. height, S.A =
(C) A cylinder with diameter of 14 cm. and height 80 cm., S.A =
(D) A sphere with radius of 14 cm., S.A =
Choose the correct answer from the options given below:
2026: 26 May Shift 1
Geometry
Solids
Medium
Consider the surface area of the following solids.
(A) A cube of edge 8 cm.
(B) A cylinder with a diameter of base 10 cm and height 42 cm.
(C) A hemisphere with 14 cm diameter.
(D) A sphere with a radius 21 cm.
Arrange the above in decreasing order.
Choose the correct answer from the options given below:
2026: 26 May Shift 1
Geometry
Solids
Medium
A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. Find the difference between the surface areas (in cm²) of two solids.
2026: 25 May Shift 2
Geometry
Solids
Easy
The surface area of a cube is 1734 , its volume is :
2026: 25 May Shift 2
Geometry
Solids
Easy
The diagonal of a cube is cm. Its surface area and volume, are:
2026: 25 May Shift 1
Geometry
Solids
Easy
Find the surface area of a sphere of radius 10.5 cm?
2026: 24 May Shift 1
Geometry
Solids
Easy
The radius of cylinder is 7 cm and height is 11 cm. The total surface area of cylinder will be:
2026: 22 May Shift 2
Geometry
Solids
Easy
If the diagonal of a cube is cm then the volume of cube is :
2026: 21 May Shift 2
Geometry
Solids
Easy
Two cubes have their volumes in the ratio 1:27. The ratio of their surface areas is?
2026: 21 May Shift 2
Geometry
Solids
Medium
A metallic sphere of radius 6 cm is melted and recast into a cone of radius 4 cm. Find the height of the cone.
2026: 21 May Shift 1
Geometry
Solids
Hard
Consider the surface areas of the following solids:
(A) A cuboid of 10 cm long, 7 cm broad, and 5 cm high.
(B) A cylinder of radius 3.5 cm and height 60 cm.
(C) A cone of radius 6 cm and height 8 cm.
(D) A sphere of radius 12 cm.
Arrange the above in decreasing order.
2026: 20 May Shift 2
Geometry
Solids
Easy
A right circular cylinder has radius 7 cm and height 10 cm. Another cylinder has twice the height and half the radius. The ratio of their volumes (first : second) is:
2026: 20 May Shift 2
Geometry
Solids
Easy
A cube has a total surface area of 384 . What is the volume of the cube?
2026: 20 May Shift 1
Geometry
Solids
Easy
The number of iron balls, each 1 cm in radius, that can be made from an iron sphere of diameter 12 cm is:
2026: 19 May Shift 2
Geometry
Solids
Easy
A rectangular block with a volume of 250 cm³ was sliced into two cubes of equal volume. How much greater (in sq.cm) is the combined surface area of the two cubes than the original surface area of the rectangular block?
2026: 18 May Shift 2
Geometry
Solids
Easy
A hemisphere of radius 4 cm is cut from a solid sphere of radius 4 cm. What is the remaining volume of the sphere? (Use )
2026: 18 May Shift 2
Geometry
Solids
Medium
Consider the surface area of the following solids.
A. A cube of edge 9 cm.
B. A cuboid of edges 18 cm, 14 cm and 7 cm.
C. A cylinder with radius of 14 cm and height 80 cm.
D. A sphere with radius of 14 cm.
Arrange the above in decreasing order.
2026: 18 May Shift 1
Geometry
Solids
Medium
A rectangular sheet 50 cm by 30 cm is rolled along the 30 cm side to form a cylinder (open at both ends). The radius of the cylinder is:
2026: 18 May Shift 1
Geometry
Solids
Hard
Consider the surface areas of the following solids.
(A) A cuboid of 12 cm long, 7 cm broad, and 5 cm high.
(B) A cylinder of radius 3.5 cm and height 60 cm.
(C) A cone of radius 6 cm and height 8 cm.
(D) A sphere of radius 12.5 cm.
Arrange the above in decreasing order.
2026: 14 May Shift 2
Geometry
Solids
Medium
Consider the surface area of the following solids.
A. A cube of edge 4 cm.
B. A cylinder with a diameter of base 14 cm and height 35 cm.
C. A hemisphere with 28 cm diameter.
D. A sphere with a radius of 7 cm.
Arrange the above in decreasing order and choose the correct answer from the options given below:
2026: 14 May Shift 1
Geometry
Solids
Medium
A cone of the height 54 cm and radius of the base of 4 cm is made up of clay. Aditya reshapes it in the form of a sphere. The radius of the sphere will be
2026: 14 May Shift 1
Geometry
Solids
Easy
If r represent the radius and h denotes the height of the solid. Then, Match List-I with List-II
| LIST-I (Solid) | LIST-II (Volume) |
|---|---|
| A. Cylinder | I. |
| B. Cone | II. |
| C. Sphere | III. |
| D. Hemisphere | IV. |
Choose the correct answer from the options given below:
2026: 12 May Shift 2
Geometry
Solids
Medium
How many iron rods, each of length 7 meter, and diameter 2 cm can be made out of 0.88 cubic meter of iron?