Exact Science - Problem of the Day - 94

94

Margie's winning art design is shown. The smallest circle has radius 2 cm, with each successive circle's radius increasing by 2 cm.

Which of the following is closest to the percent of the design that is black?

A. 42 B. 44 C. 45 D. 46 E. 48

Answer

A. 42

SOLUTIOn

Let the smallest circle be 1, the second smallest circle be 2, the third smallest circle be 3, etc.

\[\begin{array}{c|cc} \text{circle \#} & \text{radius} & \text{area} \\ \hline 1 & 2 & 4\pi \\ 2 & 4 & 16\pi \\ 3 & 6 & 36\pi \\ 4 & 8 & 64\pi \\ 5 & 10 & 100\pi \\ 6 & 12 & 144\pi \end{array}\]

The entire circle's area is

The area of the black regions is

$(100-64)\pi + (36-16)\pi + 4\pi = 60\pi$

The percentage of the design that is black is

$\frac{60\pi}{144\pi} = \frac{5}{12} \approx \boxed{\textbf{(A)}\ 42}$

‍

Subscribe to receive updates!

Be up-to-date with our recent updates, new problems and answers!

Thank you! Your submission has been received!

Oops! Something went wrong while submitting the form.

Our courses

Mathematics

Online

Curriculum Mathematics

Our goal at this course is to enhance our students’ mathematical intuition by focusing on a deep understanding of mathematical concepts and to enable them to link different concepts and apply their knowledge to solve mathematical problems to help them to improve their performance at Maths exams.

Mathematics

Online

Olympiad Mathematics

Olympiad Mathematics is a comprehensive course designed to help students win UKMT competitions. It is suitable for high-achieving mathematics students who are looking to take their skills to the next level.

Programming

Online

Introduction to Python with Turtle

This course guides you through the fundamentals of Python programming using an interactive Python library known as Turtle.

Programming

Online

Coding in Python

Python is a versatile and widely-used programming language that is particularly well-suited for beginners. It is known for its simplicity and readability, making it a great choice for students who are new to coding.

Programming

Online

16+

Data Science

This course is designed for those with little or no prior programming or data science experience, but who are eager to learn how to use Python to analyze and visualize data.

Chess

Online

Chess

Supercharge your potential by studying chess alongside maths and programming. Boost strategic thinking, problem-solving, and concentration. Unleash your competitive edge and unlock endless possibilities in these fields.

Geometry

Online

12+

Olympiad Geometry

This course encompasses a range of Geometry topics such as coordinate and spatial geometry, introductory trigonometry, angles, parallel lines, congruent and similar triangles, polygons, circles, the Pythagorean Theorem, and more. Emphasis will be placed on reinforcing Algebra skills and enhancing critical thinking through problem-solving in both mathematical and real-world contexts.

Get ready for olympiads with free problems, extracurricular topics and our courses

Mathematics

Learn more

Programming

Learn more

Where do you hold your classes?

We hold our classes online or on-site on Saturdays at our branch in Pimlico Academy, London.
You can find our timetable here.

What do you need to start learning online?

For lessons you only need a computer or phone with a microphone, camera and Internet access. Wherever you are - in London, Nottingham, New York or Bali - online lessons will be at hand.

When can I take the introductory lesson?

You can get acquainted with the school at any time convenient for you. To do this, just leave a request and sign up for a lesson.

I can't attend class, what should I do?

It is OK, it happens! Students have the opportunity to cancel a lesson up to 8 hours before the scheduled time without loss of payment. So you can reschedule it for a convenient time, and the teacher will have the opportunity to

I don't have much free time, will I have time to study?

Learning can take place at your own pace. We will select a convenient schedule and at any time we will help you change the schedule, take a break or adjust the program.

How long is one lesson?

All classes last 1 hour.

Hear from some of our amazing students who already achieved incredible results with us!

"Olympiad Maths Lessons helped me a lot to get the Gold medal in Junior Maths Challenge"

St. Paul's Student

"Thanks to the 'Data Science' and 'Coding in Python' lessons I got accepted to my dream university."

Michael

Data Science Student
Warwick University

"Great courses, which thoroughly explained topics beyond the capability of the GCSE answer sheet. Thanks so much."

Ivan

GCSE Student in Dubai

"Financial Mathematics! Best course to understand Python and Mathematics behind Finance!"

Gleb

VC Investor

"We got silver in PMC! Thanks George!"

Mum of St. Paul's Student

Prepare for the Primary Maths Challenge

"My daughter took a batch of 10 classes with George to understand Python with Turtle. I found George extremely knowledgeable and accessible."

Dad of Latymer School Student

Python with Turtle

Contact us

Email

george@exactscience.co
‍

Phone

Mon-Sun from 8am to 9pm

+44 77 07 547 144

Office

Come say hello at our office HQ.

84 Eccleston Square, Pimlico, London SW1V 1NP, UK

...or ask us anything

Smaller 3D model of a student sitting at his desk and preparing for competitions, exams and olympiads.

Ask about our courses and offerings, and we will help you choose what works best for you.

Thank you! Your submission has been received!

Oops! Something went wrong while submitting the form.