What is Conversion of Solids? | Simple Explanation for Class 6

S3-SA2-0438

What is the Conversion of Solids?

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The conversion of solids refers to changing a solid object from one geometric shape to another, usually by melting and reshaping, or by cutting and joining. The key idea is that the total volume of the solid remains the same during this transformation, even if its shape changes.

Simple Example

Quick Example

Imagine you have a lump of clay shaped like a cube. If you reshape this clay into a sphere, the amount of clay you have (its volume) does not change, only its outer shape is different. This is a simple example of converting a solid from one shape to another while keeping its volume constant.

Worked Example

Step-by-Step

PROBLEM: A cylindrical metal rod has a radius of 7 cm and a height of 10 cm. If this rod is melted and recast into small spherical balls, each with a radius of 3.5 cm, how many spherical balls can be made?

STEP 1: Find the volume of the cylindrical rod.
Volume of cylinder = pi * r^2 * h
Volume = (22/7) * (7)^2 * 10
Volume = (22/7) * 49 * 10
Volume = 22 * 7 * 10 = 1540 cubic cm

---

STEP 2: Find the volume of one spherical ball.
Volume of sphere = (4/3) * pi * r^3
Volume = (4/3) * (22/7) * (3.5)^3
Volume = (4/3) * (22/7) * 42.875
Volume = (4/3) * 22 * 6.125 = 179.666... / 3 = 179.666... / 3 = 89.833 cubic cm (approx)

---

STEP 3: Divide the total volume of the cylinder by the volume of one sphere to find the number of balls.
Number of balls = Volume of cylinder / Volume of one sphere
Number of balls = 1540 / 89.833
Number of balls = 17.14 (approx)

---

STEP 4: Since you cannot make a fraction of a ball, round down to the nearest whole number.
Answer: Approximately 17 spherical balls can be made.

Why It Matters

Understanding solid conversion is crucial in engineering and manufacturing, where materials are reshaped for different purposes. It's used by architects to design buildings and by data scientists to model how materials behave. This concept is fundamental for careers in product design, civil engineering, and even creating realistic 3D graphics in computer science.

Common Mistakes

MISTAKE: Assuming the surface area remains the same during conversion. | CORRECTION: Only the volume remains constant when a solid is converted from one shape to another. The surface area almost always changes.

MISTAKE: Forgetting to use the correct volume formula for each shape. | CORRECTION: Always double-check and use the correct formula for the volume of a cylinder, cone, sphere, cuboid, etc., before starting calculations.

MISTAKE: Not converting all units to be consistent (e.g., mixing cm and m). | CORRECTION: Ensure all measurements (radius, height, length, breadth) are in the same unit before applying any formulas.

Practice Questions

Try It Yourself

QUESTION: A cuboid of dimensions 10 cm x 8 cm x 5 cm is melted and recast into a cube. What will be the side length of the new cube? | ANSWER: Volume of cuboid = 10 * 8 * 5 = 400 cubic cm. Volume of cube = side^3. So, side^3 = 400. Side = cube root of 400 = 7.368 cm (approx).

QUESTION: A metallic sphere of radius 6 cm is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 cm, find its radius. (Hint: A wire is a cylinder). | ANSWER: Volume of sphere = (4/3) * pi * (6)^3 = (4/3) * pi * 216 = 288 * pi cubic cm. Volume of wire (cylinder) = pi * r^2 * h. So, 288 * pi = pi * r^2 * 36. 288 = r^2 * 36. r^2 = 288 / 36 = 8. r = sqrt(8) = 2.828 cm (approx).

QUESTION: A hollow sphere with an outer radius of 10 cm and an inner radius of 6 cm is melted to form a solid cylinder of height 8 cm. What is the radius of the cylinder? | ANSWER: Volume of hollow sphere = Volume of outer sphere - Volume of inner sphere = (4/3)*pi*(10)^3 - (4/3)*pi*(6)^3 = (4/3)*pi*(1000 - 216) = (4/3)*pi*784 cubic cm. Volume of cylinder = pi*r^2*h. So, (4/3)*pi*784 = pi*r^2*8. (4/3)*784 = r^2*8. 3136/3 = r^2*8. r^2 = (3136/3) / 8 = 392/3 = 130.66. r = sqrt(130.66) = 11.43 cm (approx).

MCQ

Quick Quiz

When a solid is melted and recast into a new shape, which property remains constant?

Surface Area

Volume

Colour

Shape

The Correct Answer Is:

When a solid is converted, its volume (the amount of space it occupies) stays the same because no material is added or removed. Its surface area, colour, and shape typically change.

Real World Connection

In the Real World

In Indian industries, like jewellery making, goldsmiths often melt old gold ornaments (which are solid objects) and reshape them into new designs. They need to ensure the weight (and thus the volume) of the gold remains the same to calculate its value correctly. Similarly, in construction, engineers calculate how many bricks or how much concrete is needed to fill a certain volume for a pillar or beam.

Key Vocabulary

Key Terms

VOLUME: The amount of space a three-dimensional object occupies. | CYLINDER: A solid shape with two parallel circular bases and a curved surface. | SPHERE: A perfectly round three-dimensional object, like a ball. | RECAST: To melt a metal object and form it into a different shape. | CUBIC UNITS: Units used to measure volume, such as cubic cm (cm^3) or cubic m (m^3).

What's Next

What to Learn Next

Great job understanding solid conversion! Next, you can explore how to calculate the surface areas of different 3D shapes. This will help you understand how the outer covering of objects changes even when their volume remains the same.