50+ Area and Circumference of a Circle worksheets for 6th Year on ... - Free Printable

I'll work through each question step by step, showing my calculations before providing the final answers.

Question 1:
- Diameter = 50 cm
- Formula for circumference: C = π × d (or C = 2πr)
- Using π ≈ 3.14
- C = 3.14 × 50 = 157 cm

Let me verify: 3.14 × 50 = 157 ✓

Answer: D) 157 cm

Question 2:
- Diameter = 30 meters
- Using π = 3.14
- C = π × d = 3.14 × 30
- C = 94.2 m

Let me verify: 3.14 × 30 = 94.2 ✓

Answer: D) 94.2 m

Question 3:
- Radius = 3 feet
- Formula: C = 2πr
- C = 2 × π × 3 = 6π ft

Let me check the numerical value too:
- 6π = 6 × 3.14 = 18.84 ft

Looking at the options:
- A) 3π ft = wrong formula
- B) 20.84 ft = incorrect calculation
- C) 6π ft = correct exact answer
- D) 51.96 ft = way too large

The question asks "which is closest" but option C gives the exact answer in terms of π.

Answer: C) 6π ft

Question 4:
- Diameter = 4 inches
- The formula for circumference when you have diameter is: C = π × d

Let me check each option:
- A) Divide diameter by 2 and multiply by π → This would give πr, not 2πr or πd. Wrong.
- B) Multiply diameter by 2π → This would give 2πd, which is wrong.
- C) Multiply diameter by π → This gives πd, which is correct! ✓
- D) Divide diameter by 2, square it, multiply by π → This is the area formula (πr²). Wrong.

Answer: C) Multiply the diameter by π.

Question 5:
- Diameter = 10 feet
- Need to find AREA, not circumference
- First, find radius: r = d/2 = 10/2 = 5 feet
- Formula for area: A = πr²
- A = π × 5² = π × 25 = 25π

But wait - the answer choices are in square inches (in²), not square feet!
Let me convert:
- 1 foot = 12 inches
- 10 feet = 120 inches (diameter)
- Radius = 60 inches
- A = π × 60² = π × 3600 = 3600π in²

Hmm, that doesn't match either answer choice. Let me reconsider...

Actually, looking more carefully at the problem, maybe they want us to use a different approach or there's an error in my interpretation. Let me try using π ≈ 3.14:
- If diameter = 10 feet = 120 inches
- Radius = 60 inches
- A = 3.14 × 60² = 3.14 × 3600 = 11,304 in²

That's still not matching. Let me check if perhaps the problem means something else, or if I should calculate differently.

Wait - let me re-read. It says "about 10 feet long" for diameter. Maybe they want us to work in feet first then convert?

In feet:
- A = π × 5² = 25π ≈ 78.5 sq ft

To convert sq ft to sq in: 78.5 × 144 = 11,304 in²

Still doesn't match. Let me try another interpretation - what if they made an error and meant to ask for the answer in square feet but wrote square inches?

If we ignore the unit conversion issue and just calculate with the numbers given:
- Diameter = 10 (treating as if it were in some unit)
- Radius = 5
- A = π × 25 ≈ 78.5

That matches option A! So it seems like there might be a typo in the units, or they're testing if you recognize 25π ≈ 78.5.

Answer: A) 78.5 in²

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Final Answer:
1. D) 157 cm
2. D) 94.2 m
3. C) 6π ft
4. C) Multiply the diameter by π.
5. A) 78.5 in²