Problem Set 29 – Radius and DiameterClass 5 Maths · Chapter 7 Circles · Problem Set 29 – Maharashtra Board

Summary: Problem Set 29 – Radius and Diameter

A diameter passes through the centre, so it is made of two radii joined in a straight line.

So the diameter is twice the radius: diameter = 2 × radius.

And the radius is half the diameter: radius = diameter ÷ 2.

All diameters of one circle are equal, just as all its radii are equal.

Paper test: fold a paper circle along a diameter, then fold again so the two ends meet — the two radii lie exactly on each other.

Key points to remember

• Diameter = radius + radius
• Diameter = 2 × radius
• Radius = diameter ÷ 2
• All diameters of a circle are equal
• All radii of a circle are equal
• Radius 1 cm → diameter 2 cm
• Diameter 10 cm → radius 5 cm
• Folding shows the two radii match

Problem Set 29 – Radius and Diameter – Notes

1. Two radii make one diameter

• Let O be the centre and KL a diameter. Then OK and OL are both radii.
• KL = OK + OL. Both parts are radii, so they are equal.
• That is why a diameter is twice as long as a radius.

2. Radius → diameter

• Multiply the radius by 2.
• Radius 3 cm → diameter 3 × 2 = 6 cm.
• Radius 7 cm → diameter 7 × 2 = 14 cm.

3. Diameter → radius

• Divide the diameter by 2.
• Diameter 8 cm → radius 8 ÷ 2 = 4 cm.
• Diameter 20 cm → radius 20 ÷ 2 = 10 cm.

4. Check with a paper circle

• Draw a circle, cut it out and mark its centre P.
• Draw a diameter AB. Fold the circle along AB.
• Fold it again at P so that B lands on A. Radius PB lies exactly on radius PA — each radius is half of AB.

5. All diameters are equal

• Draw two different diameters in the same circle and measure them.
• They have the same length, because each one is two radii long.
• So one circle has one radius length and one diameter length.

Formulas at a glance

Key terms

Problem Set 29 – Radius and Diameter – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 29 – Radius and Diameter – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 29 – Radius and Diameter

⏱ About 20 minutes

1. Learn (5 min)
   Learn: diameter = 2 × radius and radius = diameter ÷ 2.
2. Measure (10 min)
   Draw 3 circles, measure a radius and a diameter in each, and check the rule. Try the paper-folding test.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.