Area and Circumference calculation

Dr Zonga is organising a party and needs your help...

QUESTION 1 (MEDIUM):Dr Zonga wants to put out some cool cube-seats for guests along the back wall of Zonga Castle. The wall is 130 metres long and the seats are 40cms in width. How many seats can be place if there should be social distancing of 1.5 metres between each cube?

QUESTION 2 (HARD): Dr Zonga wants to put bunting along the same wall. He attaches the ends of the bunting at the ground level at the two ends of the wall. In the middle, the bunting will be attached to the wall 10 metres high. Bunting is sold in metres. What is the smallest number of metres Dr Zonga can buy?

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DR ZONGA LOVES PLAYING FOOTBALL...

... and during lockdown he has been finding new ways to train. Today, he tied a skipping rope to the top corners of the goal to create two targets shaped as triangles (see pic but assume EXACT triangles...). He made sure both were the same dimensions – 50cm x 50cm.

As another awesome shot flew into a triangle, he wondered…,

QUESTION 1: What % of the goal-mouth is covered by those two triangles. Can you help him solve that?

QUESTION 2: While Dr Zonga plays, he often dreams of life as a professional footballer. His thoughts turned to the weekend's games:

AWAY WIN ODDS

Arsenal v Aston Villa 2/1

Fulham v West Ham 2/1

Liverpool v Man City 11/10

Dr Zonga thinks there will be three away wins. Based on the above odds, how much would Dr Zonga win if he placed a £1 bet on this and all three away teams did actually win?

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First solved in Switzerland by Julian

First solved in UK by Tasfiha

Dartboards not whiteboards

Dr Zonga is on a mission – more dartboards in the classroom!

Playing darts can help children learn in so many ways (maths, hand-eye coordination, not poking your friend/enemy with a pointy thing,...). So these questions are part of our wider campaign to see more dartboards in school. Support us, by answering them 😊:

Question 1: I have 151 remaining. How can I get out (finish) using just 3 darts, assuming I have to hit a double or a bulls-eye with my last dart?

Question 2: The product of all of the prime numbers around the dartboard is?

Question 3: The bulls-eye on Dr Zonga's dartboard has a diameter of 1.5cm, and the dartboard itself has a radius of 23cm. Calculate the area of the dartboard outside of the bulls-eye.

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We Love running

Dr Zonga loves to run. Every day he follows the same routine - he runs to the park, three times around its perimeter (which could also be called its circumference, as it is a perfect circle) and then he heads back. Every day, Dr zonga meets friends exactly half way back home and stops there to stretch out.

Assumptions:

Distance from house to park: 850 metres

Radius of park: 400m

Question: How far, in metres, does Dr Zonga run each day?

Bonus Question: Check out our 'Live at 5' video. Estimate how far Dean runs on the treadmill during the video (metres, not steps)

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This solution was given LIVE on Instagram, 5pm (CET), 26th March 2021. @Dr_Zonga.

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fancy a Pizza?

Additional Information

So, you're in a pizzeria, about to order a large pizza. Then, you notice that the mediums are on special offer! Two mediums are the same price as one large.

Question: Which do you order, assuming:

a) You care only about how much pizza you get to eat

b) You care only about how long a crust you get (you ❤ crusts!)

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Spirals

Taking a sip of his tea, Dr Zonga pondered on how to measure the length of the spiral on his tea-coaster.

Question: The image on the right is a slightly easier spiral to work with. Assuming each square is 1cm in length, what is the circumference of the spiral?

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The solution was given LIVE on Instagram, 5pm (CET), 4th June 2021.

Click here to watch