What is Conversion of Solids?

S3-SA2-0147

Grade Level:

Class 7

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

Definition

What is it?

Conversion of solids means changing a solid object from one shape to another without changing its total volume. Imagine reshaping a lump of clay – its form changes, but the amount of clay remains the same.

Simple Example

Quick Example

If you melt an ice cube (a cube shape) and then freeze the water in a spherical mould, you've converted the ice from a cube to a sphere. The amount of water (its volume) stays the same, only its shape changes.

Worked Example

Step-by-Step

PROBLEM: A cylindrical candle with a radius of 2 cm and a height of 10 cm is melted and reshaped into spherical candles, each with a radius of 1 cm. How many spherical candles can be made?
---STEP 1: Find the volume of the cylindrical candle.
Volume of cylinder = pi * r^2 * h
Volume = pi * (2 cm)^2 * 10 cm = pi * 4 cm^2 * 10 cm = 40pi cubic cm.
---STEP 2: Find the volume of one spherical candle.
Volume of sphere = (4/3) * pi * r^3
Volume = (4/3) * pi * (1 cm)^3 = (4/3) * pi * 1 cubic cm = (4/3)pi cubic cm.
---STEP 3: Divide the total volume of the cylindrical candle by the volume of one spherical candle to find the number of spherical candles.
Number of candles = (Volume of cylinder) / (Volume of one sphere)
Number of candles = (40pi cubic cm) / ((4/3)pi cubic cm)
Number of candles = 40 / (4/3) = 40 * (3/4) = 10 * 3 = 30.
---ANSWER: 30 spherical candles can be made.

Why It Matters

Understanding solid conversion is crucial in fields like engineering and manufacturing, where materials are constantly reshaped for different purposes. Architects use it to calculate material needs, and even game developers use these principles to design virtual objects, making this concept important for future innovators.

Common Mistakes

MISTAKE: Forgetting that volume remains constant during conversion. | CORRECTION: Always remember that the total amount of material (volume) does not change, only its shape.

MISTAKE: Using the wrong formula for the volume of a shape. | CORRECTION: Double-check and memorize the correct volume formulas for cylinders, cones, spheres, and cubes before solving problems.

MISTAKE: Not converting all units to be the same (e.g., cm and m). | CORRECTION: Ensure all measurements are in the same units (e.g., all in cm or all in m) before starting calculations to avoid errors.

Practice Questions

Try It Yourself

QUESTION: A metallic sphere of radius 3 cm is melted and recast into a cylinder of radius 2 cm. What is the height of the cylinder? | ANSWER: 9 cm

QUESTION: A cone of height 24 cm and radius of base 6 cm is made from a metallic sphere. Find the radius of the sphere. | ANSWER: 6 cm

QUESTION: How many spherical bullets, each of 0.5 cm diameter, can be made from a solid cuboid of dimensions 11 cm x 10 cm x 7 cm? (Use pi = 22/7) | ANSWER: 8400 bullets

MCQ

Quick Quiz

When a solid is converted from one shape to another, what property remains unchanged?

Surface Area

Volume

Shape

Density

The Correct Answer Is:

When a solid is converted, its shape and surface area change. However, the amount of material, which is its volume, remains constant. Density might change if the material is compressed or expanded, but volume stays the same.

Real World Connection

In the Real World

Think about how 'mithai' (sweets) are made. A large block of 'khoya' might be shaped into different forms like 'peda' (round), 'barfi' (square), or 'laddoo' (spherical). The total amount of khoya remains the same, but its form changes. This is a perfect example of solid conversion in our daily lives.

Key Vocabulary

Key Terms

VOLUME: The amount of space occupied by a 3D object | SURFACE AREA: The total area of the outer surface of a 3D object | CYLINDER: A 3D shape with two parallel circular bases and a curved surface | SPHERE: A perfectly round 3D object, like a ball | CONE: A 3D shape with a circular base and a single vertex

What's Next

What to Learn Next

Great job understanding solid conversion! Next, you can explore 'Surface Areas and Volumes of Combinations of Solids'. This will help you calculate areas and volumes when different shapes are joined together, building on what you've learned here.