Two marbles are sitting side by side in a glass container.b the base of the container is 10 units long and the radius of the smaller marble is 2 units. What is the radius of the larger marble? Describe the strategy used to answer the question.
what does side-by-side mean?
touching?
both marbles touching a vertical line between them?
Do both marbles touch the (presumably vertical) sides of the container?
clearing up these questions will be a good place to start.
In the most reasonable scenario, marbles touching each other and the sides of the container, draw a diagram. If the radius of the larger is r, and the horizontal distance between the centers of the marbles is s,
r+s+2 = 10
(r-2)^2 + s^2 = (r+2)^2
to see this, consider the line joining the centers of the marbles.
so,
(r-2)^2 + (8-r)^2 = (r+2)^2
r = 4(3-√5) = 3.0557
Steve this makes sense to me. Thank you
I knowvitbis a lot to ask, but how do you get from
(r-2)^2 + (8-r)^2 = (+2)^2 to r=4(3-rt5)
I think he used the quadratic formula which is -b +/- rt (b^2 - 4ac) all that divided by 2a
To find the radius of the larger marble, we can use the information about the base of the container and the radius of the smaller marble.
First, let's visualize the situation. We have two marbles sitting side by side in a glass container. The base of the container is 10 units long, which means it has a diameter of 10 units. Let's represent this with a line segment.
Now, we know that the smaller marble has a radius of 2 units. Let's represent this by drawing a circle with a radius of 2 units on one side of the line segment (base of the container).
To find the radius of the larger marble, we need to determine how much space is left for the larger marble on the other side of the line segment. Since the smaller marble already occupies 4 units of space (2 units on each side), the remaining space for the larger marble is 10 units - 4 units = 6 units.
So, we can conclude that the radius of the larger marble is half of the remaining space, which is 6 units / 2 = 3 units.
In summary, the strategy used to answer the question is to consider the diameter of the base of the glass container and subtract twice the radius of the smaller marble. The remaining space is then divided by 2 to obtain the radius of the larger marble.