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: Option 1: 354 cm² Option 2: 486 cm² Option 3: 327 cm² Option 4: 419 cm²

Answer: 486 cm². Solution: Total volume = 1^3 + 6^3 + 8^3 = 1 + 216 + 512 = 729 cubic cm, so the new edge is 3√729 = 9 cm. Surface area = 6 x 9^2 = 486 square cm.

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:

354 cm²

486 cm²

327 cm²

419 cm²

✅ Correct Option: 2

Total volume $= 1^3 + 6^3 + 8^3 = 1 + 216 + 512 = 729$ cubic cm, so the new edge is $\sqrt[3]{729} = 9$ cm. Surface area $= 6 \times 9^2 = 486$ square cm.

2026: 26 May Shift 1

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.

(D) A sphere with a radius 21 cm.

Arrange the above in decreasing order.

Choose the correct answer from the options given below:

2025: 3 June Shift 1

The ratio of the diameter and height of the right circular cylinder is 4 : 3. If the diameter of the cylinder is reduced 25 %, then its total surface area is reduced to 318.5π m². What is the circumference of the base of the cylinder?

2026: 20 May Shift 2

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: 24 May Shift 1

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

2025: 22 May Shift 1

Find the values and arrange in increasing order:

(A) If each edge of a cube is increased by 20%, then the percentage increase in its volume is:

(B) If the radius of a cylinder is increased by 20%, while height increase 10%, then the percentage increase in the volume of the cylinder

(D) If the radius of a sphere is increased by 10%, then the percentage increase in its volume is:

Choose the correct order:

2026: 14 May Shift 1

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. $\dfrac{2}{3}\pi r^3$
B. Cone	II. $\dfrac{4}{3}\pi r^3$
C. Sphere	III. $\dfrac{1}{3}\pi r^2 h$
D. Hemisphere	IV. $\pi r^2 h$

Choose the correct answer from the options given below:

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:

Solution

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