Mathematics
Grade 10
15 min
Multiply three numbers up to 3 digits each
Multiply three numbers up to 3 digits each
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1
Introduction & Learning Objectives
Learning Objectives
Calculate the squared radius of a circle centered at the origin given a point on its circumference.
Extract up to three distinct numerical values from the properties of given circles.
Set up a multiplication problem involving three numbers, each up to three digits.
Apply the associative and commutative properties to strategically multiply three numbers.
Accurately compute the product of three numbers, each up to 3 digits, without a calculator.
Verify the result of a large multiplication problem using estimation.
How could you compare the relative scale of three different planetary orbits without just saying one is 'bigger'? You'd need to multiply their key dimensions! 🪐
This tutorial bridges coordinate geometry with fundamental arithmetic...
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Key Concepts & Vocabulary
TermDefinitionExample
Equation of a Circle (Origin-Centered)The standard algebraic representation of a circle with its center at the origin (0,0). It is defined by the formula x² + y² = r², where (x, y) is any point on the circle and r is the radius.A circle passes through the point (5, 12). Its equation is x² + y² = 169, because 5² + 12² = 25 + 144 = 169.
Squared Radius (r²)The radius of a circle multiplied by itself. In the context of the coordinate plane, it is the sum of the squares of the x and y coordinates of any point on a circle centered at the origin.For a circle passing through the point (9, 40), the squared radius (r²) is 9² + 40² = 81 + 1600 = 1681.
ProductThe result obtained by multiplying two or more numbers together.The product of 10, 15, and 20 is 10 × 15 × 20 = 3000.
Ass...
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Core Formulas
Squared Radius Formula
r^2 = x^2 + y^2
For any circle centered at the origin (0,0) that passes through the point (x, y), this formula is used to directly calculate the squared radius without first finding the radius itself.
Product of Three Numbers
P = a \times b \times c = (a \times b) \times c = a \times (b \times c)
To find the product of three numbers, first multiply any two of them to get an intermediate product. Then, multiply that result by the third number. Use the associative and commutative properties to choose the easiest pair to multiply first.
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Challenging
The product of the squared radii of three origin-centered circles is 270,000. The first circle passes through (3, 4) and the second circle's equation is x² + y² = 144. What is the squared radius of the third circle?
A.100
B.125
C.75
D.150
Challenging
A system's stability factor is the product of three values: the radius of circle C₁ with equation x² + y² = 625, the squared radius of circle C₂ passing through (12, 16), and the radius of circle C₃ with an area of 400π. What is the stability factor?
A.100,000
B.250,000
C.1,000,000
D.200,000
Challenging
A circular gear C₁ centered at the origin has a point (12, 16) on its edge. Two other gears, C₂ and C₃, have squared radii that are the two distinct prime factors of 38. To find the system torque, you must multiply the squared radius of C₁ by the squared radii of C₂ and C₃. What is the torque value?
A.15,200
B.7,600
C.1,900
D.3,800
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