The ratio of circumference of two circles is 5:3. What is the ratio of their radius?
You can solve this for yourself. Here's how:1. Look in your math book for an equation which relates the circumference of a circle to its radius. (It's as easy as pie.)2. The most common expression uses the radius as the independent variable (the one you get to pick) and solves for the dependent variable (the one that is the "answer"). You need to algebraically express this equation so that the circumference is the independent variable, so you can solve for the radius.3. Using the form of the equation you found in Step 2, select two numbers for circumferences whose ratio is 5:3. For example, you could select 5 and 3, or 50 and 30, or 500 and 300. Use these numbers to solve for the radii of two circles and compare the radii you find as ratios. You should find the same ratio every time.
If the area of one circle is twice that of another circle, what is the ratio in percent of the smaller to larger circle?
Depends on which ratio you want to portray.If you want to show the ratio of area, 1:2 or the smaller circle if 50% the area of the larger circleIf you want to show the ratio of the radius of the circle it takes a little more work since area is [math]\pi*r^2[/math] and double that area would be [math]2*\pi*r^2[/math] so let’s look at the math.a1 = area of smaller circle and a2 is area of larger circle, r1 = radius of smaller circle and r2 = radius of larger circleso [math]a1=\pi*r1^2[/math] and [math]a2=\pi*r2^2[/math][math]a1=\frac{a2}{2}[/math] or even easier [math]a1=a2*0.5[/math] so therefore [math]\pi*r1^2 = \pi*r2^2*0.5[/math] we can factor out [math]\pi[/math] from both equations leaving us with [math]r1^2=r2^2*0.5[/math] now we need to find the square root of each side to get us r1 so [math]r1=\sqrt{r2^2*0.5}[/math] or [math]r1=r2*\sqrt{0.5}[/math] which leaves us with [math]r1 = r2 * 0.7071[/math] or the radius of the smaller circle being 70.71% of the larger circle and consequently, that would be the same difference in percentage of the circumference since [math]c=\pi*2*r[/math]
If the ratio of the radii of two circles is 3:4, then what is the ratio of their areas?
9:16
If the surface area of two similar cones is at the ratio 4:9 ,then what is the ratio of their volumes?
[math]A2A[/math]Yes, you are correct and the reasoning is simpleI'm assuming that "identical" here refers to "similar"The two triangles are similar (AA)Therefore, [math]\dfrac{r}{R}=\dfrac{h}{H}=\dfrac{l}{L}[/math]ratio of surface areas [math]= \dfrac{\pi r l}{\pi R L} =\dfrac{r}{R}\dfrac{l}{L} =\dfrac{r^2}{R^2}=\dfrac{4}{9}[/math]therefore, [math]\boxed{\dfrac{r}{R}=\dfrac{2}{3}}[/math]Now for volume,ratio [math]= \dfrac{\pi r^2 h}{\pi R^2 H}=\dfrac{r^2}{R^2}\dfrac{h}{H}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{2}{3}\right)^3=\boxed{\dfrac{8}{27}}[/math]Hope it helps!
How do you find the scale factor of two numbers?
Haha!!!!!! Next time you can find someone in your class and ask the question. But being a good Samaritan and also I suppose maybe you didnt want your friends to know you were day-dreaming, here are my replies : 1) Scale factor is basically the fraction of one number with the other. Can be expressed in ratio form as well. So 84/6 is 14 : 1 or just 14. 2) So now you got the idea? Again 5 and 1.5 the scale factor is 10/3 or in ratio form 10: 3 RegardZ Edem
If the circumference of circle P and circle Q is 5:4 in ratio, what is the ratio of the area of both circles?
25:16Let's have two circles. Let's make one have a radius of 5, one a radius of 4. Well what's the circumference of the first one? It's 10 pi, while the other circle has a circumference is 8 pi. 10:8 = 5:4 So this satisfies your requirement. Notice the ratio of the radi is the ratio of circumferences.Let's find the ratio of both areas. We get 25pi and 16 pi, so when we divide, the pi cancels out.The reason for this ratio is that whenever you have a ratio of a side length in two shapes, (radius for circle, sidelength for square etc) the 1-D measure will always be the same ratio as the same lengths. The one D measure is perimeter the circumference. The 2-D measure will be the ratio squared, and this is area. The 3-D measure is the ratio cubed, and this is the volume. This works because it uses the fact of how many times the side is in the calculation.
The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding medians. Can someone tell me the proof?
I was looking for an answer myself and thought of using Heron's theorem to see how the areas of similar triangles relate.Heron's theorem is a way to calculate the area of a triangle given its side lengths. If [math]a,b,c[/math] are the side length of a triangle, it's area is equal to [math]\sqrt{p(p-a)(p-b)(p-c)}[/math] where [math]p=\frac{a+b+c}{2}[/math].Let T1 and T2 be two similar triangles with side lengths [math]A,B,C[/math] and [math]a,b,c[/math]. The squared-area of the first triangle is [math]P(P-A)(P-B)(P-C)[/math]. Since the two triangles are similar, there exists some [math]k=A/a=B/b=C/c[/math].Now [math]P = (A+B+C)/2 = (ka + kb + kc)/2 = kp[/math]. Substitute [math]P[/math] by [math]kp[/math] and [math]A[/math] by [math]ka[/math]...We get [math]P(P-A)(P-B)(P-C) = [/math][math] k^4 p(p-a)(p-b)(p-c)[/math]. Take square roots and you get the answer.
I could really use some help on these math questions, can somebody please help me?
1. Circle 1 has center (−6, 2) and a radius of 8 cm. Circle 2 has center (−1, −4) and a radius 6 cm. What transformations can be applied to Circle 1 to prove that the circles are similar? It's asking me to fill in the blanks for this: The circles are similar because the transformation rule (___,___) can be applied to Circle 1 and then dilate it using a scale factor of (__/__). 2. Why is circle 1 similar to circle 2? Circle 1: center (−1, 10) and radius 4.8 Circle 2: center (−1, 10) and radius 1.2 A) Circle 1 is a dilation of circle 2 with a scale factor of 4. B) Circle 1 and circle 2 have the same center. C) Circle 2 is a dilation of circle 1 with a scale factor of 3.6. D) Circle 1 is congruent to circle 2. 3. Which transformations can be used to show that circle M is similar to circle N? Circle M: center (−1, 10) and radius 3 Circle N: center (0, 10) and radius 15 A) Circle N is a translation of circle M, 1 unit right. B) Circle M is a dilation of circle N with a scale factor of 12. C) Circle N is a dilation of circle M with a scale factor of 5. D) Circle M and circle N are congruent. (You can choose more than one answer on this question.)
If the diameter of a circle increases by 10%,by how much does its area increase by?
Whatever we increase the diameter by, we also increase the radius by the same length. By this logic, we know that if the diameter is increased by 10%, then so is the length of the radius. Since we don’t know the length of the radius of the original circle, we can assign it to the variable [math]r[/math]. This means that the length of the new radius is equivalent to [math]1.1r.[/math]Then, we can substitute the value of the new radius in the equation [math]πr^2[/math] to find the percentage increase in the area. Solving for this expression, we get [math]1.21π[/math]. This tells us that the total area of the circle increases by 21% when the diameter is increased by 10%.[math]\boxed{21 \%}[/math]