Solve Quadratic Equation: Ratio of Two Cones' Radii

  • MHB
  • Thread starter Monoxdifly
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So, in summary, Azis wants to make two cones using cartons, with the first cone having twice the surface area and side length of the second cone. The ratio of their radii is 4, taking into account the base area.
  • #1
Monoxdifly
MHB
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Azis wants to make two cones using cartons. The surface area of the first cone is twice the second. The side length of the first cone is also twice the second. Determine the ratio of those cones' radius!

s1 = 2s2
L1 = 2L2
πr1(r1 + s1) = 2πr2(r2 + s2)
r1(r1 + 2s2) = 2r2(r2 + s2)

I was stuck with quadratic equations...
 
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  • #2
Monoxdifly said:
Azis wants to make two cones using cartons. The surface area of the first cone is twice the second. The side length of the first cone is also twice the second. Determine the ratio of those cones' radius!

s1 = 2s2
L1 = 2L2
πr1(r1 + s1) = 2πr2(r2 + s2)
r1(r1 + 2s2) = 2r2(r2 + s2)

I was stuck with quadratic equations...
$A_1 = 2A_2 \implies \pi r_1 \cdot L_1 = 2\pi r_2 \cdot L_2 \implies \pi r_1 \cdot L_1 = 2\pi r_2 \cdot 2L_1 \implies \dfrac{r_1}{r_2} = 4$
 
  • #3
But we must take into account the base area...
 

FAQ: Solve Quadratic Equation: Ratio of Two Cones' Radii

What is a quadratic equation?

A quadratic equation is an equation that contains a variable raised to the second power, also known as a squared term. It is typically written in the form of ax^2 + bx + c = 0, where a, b, and c are constants.

What is the ratio of two cones' radii?

The ratio of two cones' radii is the comparison between the size of the two cones' base circles. It is expressed as a fraction, with the larger radius on top and the smaller radius on the bottom.

How do I solve a quadratic equation?

To solve a quadratic equation, you can use the quadratic formula which is -b ± √(b^2 - 4ac) / 2a, where a, b, and c are the coefficients from the equation. You can also factor the equation or use the completing the square method.

What is the significance of the ratio of two cones' radii?

The ratio of two cones' radii is significant because it determines the relative size of the two cones' base circles. This can be useful in various real-life applications, such as calculating the volume or surface area of the cones.

Can the ratio of two cones' radii be negative or zero?

Yes, the ratio of two cones' radii can be negative or zero. This can happen if the larger radius is negative or if one of the radii is zero. However, in most cases, the ratio will be a positive number as both radii are typically positive values.

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