Q1:

2026: 6 June Shift 1

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:

Answer options
Option 3
Correct Answer
Explanation for 2026: 6 June Shift 1 GET question 1

Q2:

2026: 31 May Shift 2

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:

Answer options
Option 2
Correct Answer
Explanation for 2026: 31 May Shift 2 GET question 2

Q3:

2026: 31 May Shift 2

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?

Answer options
Option 3
Correct Answer
Explanation for 2026: 31 May Shift 2 GET question 3

Q4:

2026: 31 May Shift 1

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:

Answer options
Option 4
Correct Answer
Explanation for 2026: 31 May Shift 1 GET question 4

Q5:

2026: 30 May Shift 2

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:

Answer options
Option 4
Correct Answer
Explanation for 2026: 30 May Shift 2 GET question 5

Q6:

2026: 30 May Shift 1

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?

Answer options
Option 1
Correct Answer
Explanation for 2026: 30 May Shift 1 GET question 6

Q8:

2026: 29 May Shift 1

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 = 486 cm2486 \text{ cm}^2

(B) A cuboid of 18 cm. long, 14 cm. width and 7 cm. height, S.A = 108 cm2108 \text{ cm}^2

(C) A cylinder with diameter of 14 cm. and height 80 cm., S.A = 3520 cm23520 \text{ cm}^2

(D) A sphere with radius of 14 cm., S.A = 2004 cm22004 \text{ cm}^2

Choose the correct answer from the options given below:

Answer options
Option 3
Correct Answer
Explanation for 2026: 29 May Shift 1 GET question 8

Q9:

2026: 26 May Shift 1

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:

Answer options
Option 4
Correct Answer
Explanation for 2026: 26 May Shift 1 GET question 9

Q10:

2026: 26 May Shift 1

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.

Answer options

Q11:

2026: 25 May Shift 2

Solids

Easy

The surface area of a cube is 1734 cm2cm^2, its volume is :

Answer options

Q12:

2026: 25 May Shift 2

Solids

Easy

The diagonal of a cube is 636\sqrt{3} cm. Its surface area and volume, are:

Answer options

Q14:

2026: 24 May Shift 1

Solids

Easy

The radius of cylinder is 7 cm and height is 11 cm. The total surface area of cylinder will be:

Answer options

Q17:

2026: 21 May Shift 2

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.

Answer options

Q18:

2026: 21 May Shift 1

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.

Answer options

Q19:

2026: 20 May Shift 2

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:

Answer options

Q20:

2026: 20 May Shift 2

Solids

Easy

A cube has a total surface area of 384 cm2cm^2. What is the volume of the cube?

Answer options

Q22:

2026: 19 May Shift 2

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?

Answer options

Q23:

2026: 18 May Shift 2

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 π≈3.14\pi \approx 3.14)

Answer options

Q24:

2026: 18 May Shift 2

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.

Answer options

Q25:

2026: 18 May Shift 1

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:

Answer options

Q26:

2026: 18 May Shift 1

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.

Answer options

Q27:

2026: 14 May Shift 2

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:

Answer options

Q28:

2026: 14 May Shift 1

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

Answer options

Q29:

2026: 14 May Shift 1

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. CylinderI. 23πr3\dfrac{2}{3}\pi r^3
B. ConeII. 43πr3\dfrac{4}{3}\pi r^3
C. SphereIII. 13πr2h\dfrac{1}{3}\pi r^2 h
D. HemisphereIV. πr2h\pi r^2 h

Choose the correct answer from the options given below:

Answer options