Sure! Let's start by solving Part A and Part B step by step.
A.) Surface Area
Step Arrangement:
- Step 1: Find area of each face
- Step 2: Add up areas from each face
For a cylinder, the total surface area (SA) can be calculated using the formula: \[ SA = 2\pi r^2 + 2\pi rh \] where \(r\) is the radius and \(h\) is the height. Given that the diameter is 6, the radius \(r\) will be: \[ r = \frac{diameter}{2} = \frac{6}{2} = 3 \] The height \(h\) is given as 9.
Substituting values:
- Calculate the area of the two circular bases: \[ 2\pi r^2 = 2\pi (3^2) = 2\pi \cdot 9 = 18\pi \]
- Calculate the lateral surface area: \[ 2\pi rh = 2\pi \cdot 3 \cdot 9 = 54\pi \]
- Combine the areas: \[ SA = 18\pi + 54\pi = 72\pi \]
Solve: Using \( \pi \approx 3.14 \): \[ SA \approx 72 \cdot 3.14 \approx 226.08 \]
\[ \text{Surface Area} = 72\pi \text{ or } 226.08 \text{ square units} \]
B.) Volume
Step Arrangement:
- Step 1: Find area of the base
- Step 2: Multiply area of base (B) to height
The volume (V) of a cylinder can be calculated using the formula: \[ V = B \cdot h \] where \(B = \pi r^2\) (area of the base) and \(h\) is the height.
Substituting values:
- Calculate the area of the base: \[ B = \pi r^2 = \pi (3^2) = 9\pi \]
- Multiply by height: \[ V = 9\pi \cdot 9 = 81\pi \]
Solve: Using \( \pi \approx 3.14 \): \[ V \approx 81 \cdot 3.14 \approx 254.34 \]
\[ \text{Volume} = 81\pi \text{ or } 254.34 \text{ cubic units} \]
Summary:
- Surface Area = \(72\pi\) or approximately \(226.08\) square units.
- Volume = \(81\pi\) or approximately \(254.34\) cubic units.