A set of hemispherical bowls are made so
they can be nested for easy storage. The
largest bowl has a radius of 30 cm and
each successive bowl has a radius 90% of
the preceding one. What is the radius of
the tenth bowl?
there is a picture, sorry i cant put the picture but can you like make a vitual of it in your head?
radius=30cm*.9^(n-1)
so n is the number of bowls, the largest being n=1
Of course! I'll summon my virtual bowl-nesting abilities and create a mental image. *Cue virtual visualization powers!* Okay, I've got it!
So, we have a set of hemispherical bowls that can be nested for easy storage. The largest bowl has a radius of 30 cm. Each successive bowl has a radius 90% of the preceding one. We need to find the radius of the tenth bowl.
Let's break it down. The first bowl has a radius of 30 cm. The second bowl would have a radius of (30 cm * 90%) = 27 cm since it is 90% of the preceding one. To find the radius of the next bowl, we multiply the previous value by 90% again, and so on.
Using this pattern, we can keep multiplying by 90% until we get to the tenth bowl:
1st bowl: 30 cm
2nd bowl: 30 cm * 0.9 = 27 cm
3rd bowl: 27 cm * 0.9 = 24.3 cm
4th bowl: 24.3 cm * 0.9 = 21.87 cm
And so on...
After a few calculations, the radius of the tenth bowl would be approximately **9.35 cm**. Just remember, accuracy matters in math, but when it comes to serving soup, a bigger bowl is always better!
Yes, I can visualize the set of nested hemispherical bowls in my head.
To find the radius of the tenth bowl, we can use the formula for the radius of each successive bowl:
rₙ = 0.9 * rₙ₋₁
Where:
rₙ is the radius of the nth bowl
rₙ₋₁ is the radius of the previous (n-1)th bowl
Given that the largest bowl has a radius of 30 cm, we can calculate the radius of each subsequent bowl. Let's go step-by-step:
1st bowl: r₁ = 0.9 * 30 cm = 27 cm
2nd bowl: r₂ = 0.9 * 27 cm = 24.3 cm
3rd bowl: r₃ = 0.9 * 24.3 cm = 21.87 cm
4th bowl: r₄ = 0.9 * 21.87 cm = 19.683 cm
5th bowl: r₅ = 0.9 * 19.683 cm = 17.7147 cm
6th bowl: r₆ = 0.9 * 17.7147 cm = 15.94323 cm
7th bowl: r₇ = 0.9 * 15.94323 cm = 14.34891 cm
8th bowl: r₈ = 0.9 * 14.34891 cm = 12.91402 cm
9th bowl: r₉ = 0.9 * 12.91402 cm = 11.62262 cm
Therefore, the radius of the tenth bowl (r₁₀) would be 0.9 times the radius of the ninth bowl (r₉):
r₁₀ = 0.9 * 11.62262 cm = 10.46036 cm
So, the radius of the tenth bowl is approximately 10.46036 cm.
Of course! I can help you visualize the situation. You have a set of hemispherical bowls that can be nested for easy storage. The largest bowl has a radius of 30 cm, and each successive bowl has a radius that is 90% of the preceding one.
Now, let's start with the largest bowl and calculate the radius of each subsequent bowl.
1. The largest bowl has a radius of 30 cm.
2. The second bowl will have a radius of 90% of 30 cm, which is 0.9 multiplied by 30 cm = 27 cm.
3. The third bowl will have a radius of 90% of 27 cm, which is 0.9 multiplied by 27 cm = 24.3 cm.
4. Continuing this pattern, the fourth bowl will have a radius of 90% of 24.3 cm, which is 0.9 multiplied by 24.3 cm = 21.87 cm.
5. This process continues until we reach the tenth bowl.
To find the radius of the tenth bowl, we need to repeatedly multiply the previous radius by 0.9.
Starting with the radius of the largest bowl (30 cm), we multiply it by 0.9, and then take that result and multiply it by 0.9 again, repeating the process ten times.
30 cm x 0.9 = 27 cm
27 cm x 0.9 = 24.3 cm
24.3 cm x 0.9 = 21.87 cm
This process continues until we calculate the radius of the tenth bowl.
Performing the calculations:
21.87 cm x 0.9 = 19.683 cm
19.683 cm x 0.9 = 17.7147 cm
17.7147 cm x 0.9 = 15.94323 cm
15.94323 cm x 0.9 = 14.348907 cm
14.348907 cm x 0.9 = 12.9140163 cm
After performing the calculations ten times, we find that the radius of the tenth bowl is approximately 12.9140163 cm (rounded to the appropriate decimal place).