the volume of a cylinder 288picm3 the base radius is 8 cm find its tsa leave the answer in terms of
tsa?
answer in terms of ??
terms of what? i dont get you i dont understand well i know what the question is asking but the end i am all like this
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tsa is total surface area.
r=8
v = pi r^2 h = 288pi
so, h = 288pi/64pi = 4.5
tsa is two circles plus the curved sides:
2pir^2 + 2pi r h = 2pi*r(r+h)
= 2pi*8(8+4.5) = 200pi cm^2
To find the total surface area (TSA) of a cylinder, we need two measurements: the radius of the base and the height of the cylinder. Since you have only provided the volume and the base radius, we need to find the height before calculating the TSA.
Step 1: Calculate the height of the cylinder using the provided volume.
The volume formula for a cylinder is V = πr²h, where V represents the volume, r is the radius of the base, and h is the height. Rearranging the formula, we can solve for h:
V = πr²h
288 = π(8)²h
288 = 64πh
h = 288 / (64π)
h ≈ 1.428 cm (rounded to three decimal places)
Step 2: Calculate the TSA of the cylinder using the base radius and height.
The TSA formula for a cylinder is TSA = 2πrh + 2πr², where TSA represents the total surface area, r is the radius of the base, and h is the height. Plugging in the values:
TSA = 2π(8)(1.428) + 2π(8)²
TSA = 2π(11.424) + 2π(64)
TSA = 22.848π + 128π
TSA = (22.848 + 128)π
TSA ≈ 150.848π cm²
Therefore, the total surface area (TSA) of the cylinder is approximately 150.848π cm².