Question

Find the surface area of the bulb.

Answer 1

Step 1: Understanding the Given Information:
The bulb is spherical in shape.
Diameter (d) = 7 cm

Instead of using the formula 4πr², we directly use the alternative formula:
Surface Area = πd²

Step 2: Applying the Formula:
Surface Area = π × d²
= (22/7) × 7²
= (22/7) × 49

Now simplify step-by-step:
= 22 × 7
= 154 cm²

Step 3: Final Answer:
The surface area of the bulb is 154 cm².

Answer 2

Step 1: Understanding the Condition Clearly:
The bulb must fit inside the cuboid while maintaining a gap of 1 cm from every inner face.
This means the bulb cannot touch any of the six faces of the cuboid.

So effectively, we reduce each dimension of the cuboid by 2 cm (1 cm gap on both opposite sides).

Step 2: Finding Effective Inner Dimensions:
Original dimensions:
Length = 24 cm
Width = 12 cm
Height = 17 cm

After leaving 1 cm gap on both sides:
Effective Length = 24 − 2 = 22 cm
Effective Width = 12 − 2 = 10 cm
Effective Height = 17 − 2 = 15 cm

Step 3: Determining Maximum Diameter:
A spherical bulb must fit completely inside these reduced dimensions.
Therefore, its diameter cannot exceed the smallest effective dimension.

Smallest dimension = 10 cm

Hence,
Maximum possible diameter = 10 cm

Final Answer:
The maximum diameter of the bulb is 10 cm.

Answer 3

Step 1: Understanding the Concept in Another Way:
Since the lamp is open at the top and bottom, only the four vertical rectangular faces are covered with fabric.
So instead of using perimeter directly, we calculate the area of each rectangular face separately and then add them.

Step 2: Adjusting the Height for Folds:
Actual height of lamp = 17 cm
Fold at top = 2 cm
Fold at bottom = 2 cm

Total fabric height = 17 + 2 + 2
= 21 cm

Step 3: Calculating Area of Each Face:
Two faces of size 24 × 21
Area of one such face = 24 × 21 = 504 cm²
Area of two such faces = 2 × 504 = 1008 cm²

Two faces of size 12 × 21
Area of one such face = 12 × 21 = 252 cm²
Area of two such faces = 2 × 252 = 504 cm²

Step 4: Total Fabric Area:
Total area = 1008 + 504
= 1512 cm²

Final Answer:
The area of fabric used is 1512 cm².

Answer 4

Step 1: Understanding the Structure Differently:
Instead of multiplying all three dimensions together at once, we first calculate the base area of the cuboid and then multiply it by the height.
This separates the calculation into two simple steps.

Step 2: Calculating the Base Area:
Base of cuboid is a rectangle.

Length (L) = 24 cm
Width (W) = 12 cm

Base Area = L × W
= 24 × 12
= 288 cm²

Step 3: Multiplying by Height:
Height (H) = 17 cm

Volume = Base Area × Height
= 288 × 17

Now multiply step-by-step:
288 × 17 = 288 × (10 + 7)
= 2880 + 2016
= 4896 cm³

Step 4: Final Answer:
The space available inside the lamp is 4896 cm³.