Answer:
35. Radius= 12 cm
36. (B) 50 cm
Explanation:
35.
TSA = 2πr(h+r)
Expanding the brackets, we get:
TSA = 2πrh + 2πr^2
Rearranging the equation, we get:
TSA - 2πrh = 2πr^2
Dividing both sides by 2π, we get:
r^2 = (TSA - 2πrh) / 2π
Taking the square root of both sides, we get:
r = √[(TSA - 2πrh) / 2π]
We need to simplify the given equation to solve for r.
r = √[(905.143) - 2(22/7)r(14)) / 2(22/7)]
r = √[(905.143) - (88/7)r] / (44/7)
Squaring both sides, we get:
r^2 = [(905.143) - (88/7)r] / (44/7)
Multiplying both sides by (44/7) and simplifying:
7r^2 - 88r - 905.143 = 0
Using the quadratic formula:
r = [88 ± √(88^2 - 4(7)(-905.143))] / (2(7))
r ≈ 12.009 or r ≈ -12.892
Since r represents the radius of a circle, which cannot be negative, we ignore the negative solution.
Therefore, the solution is r ≈ 12.009.
36.
We can use the formula for the volume of a cylinder:
volume = πr^2h
where r is the radius and h is the height of the cylinder.
First, we need to find the radius of the drum. The diameter is given as 56 cm, so the radius is half of that, or 28 cm.
Next, we can use the given volume of 123.2 liters. However, we need to convert liters to cubic centimeters (cm^3) since the dimensions are in centimeters.
1 liter = 1000 cm^3
So, 123.2 liters = 123,200 cm^3.
Now we can plug in the values:
123,200 cm^3 = π(28 cm)^2h
Simplifying:
123,200 cm^3 = 2464π cm^2h
Dividing both sides by 2464π cm^2:
50 cm = h
Therefore, the height of the drum is 50 cm.