These cylinders are similar. Find the surface area of the smaller cylinder. Round to the nearest tenth.
1 answer:
Answer:
Surface area = 80.4 cm²
Step-by-step explanation:
The diagram of both cylinders is attached below for a better understanding.
<h3>First find the radius of larger cylinder:</h3>Surface area = 2πrh + 2πr²
236 = 2(3.14)(5)r + 2(3.14)r²
236 = 31.4r + 6.28r²
236 = 6.28(r² + 5r)
35.58 = r² + 5r
r = 3.97 cm
<h3>Find the radius of Smaller cylinder:</h3>
Two cylinders are in proportion if their heights and radius are in proportion:
Ratio of height of small cylinder to big cylinder = 3/5 = 0.6
So ratio of radius of both is also 0.6
Let R be the radius of small cylinder
ratio of radius of small cylinder to big cylinder = R / 3.97
R = (0.6)(3.97)
R = 2.38
<h3 /><h3>Surface Area for small cylinder:</h3>R = 2.38cm and h = 3 cm
Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(2.38)(3) + 2(3.14)(2.38)²
Surface area = 80.4115cm²
Round of to nearest tenth
Surface area = 80.4 cm²
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Answer:
A) 0.99413
B) 0.00022
Step-by-step explanation:
A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:
Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes
Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:
μ = n*μ_s ample = 42 × 5 = 210 minutes
While the standard deviation for the population would be:
σ = √nσ_sample = √(42 × 6) = 15.8745 minutes
To find the z-score, we will use the formula;
z = (x - μ)/σ
Thus;
z = (250 - 210)/15.8745
z = 2.52
From the z-distribution table attached, we have;
P(Z < 2.52) ≈ 0.99413
B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.
Thus, total time is now 250 + 10 = 260 minutes
Similar to the z-formula in A above, we have;
z = (260 - 210)/15.8745
z = 3.15
P(Z > 3.15) = 0.00022
