The volume of a cylinder is 1200cm3 and the area of its base is 150cm2. Find the height of the cylinder.
Answer Details
We can use the formula for the volume of a cylinder to solve this problem, which is:
V = πr²h
where V is the volume of the cylinder, r is the radius of the base, and h is the height of the cylinder.
We are given that the volume of the cylinder is 1200cm³, so we can substitute this value into the formula:
1200 = πr²h
We are also given that the area of the base is 150cm², and the formula for the area of a circle is:
A = πr²
where A is the area of the circle and r is the radius. Since the base of the cylinder is a circle, we can use this formula to find the radius:
150 = πr²
r² = 150/π
r ≈ 6.12 cm (rounded to two decimal places)
Now we can substitute this value for r in the first formula and solve for h:
1200 = π(6.12)²h
h ≈ 8 cm (rounded to two decimal places)
Therefore, the height of the cylinder is approximately 8cm. So the correct option is (b) 8.00cm.