To find the volume and surface area of a right circular cylinder, you can use the following formulas:
-
Volume (V): \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height of the cylinder.
-
Surface Area (A): \[ A = 2\pi r(h + r) \] This includes the areas of the two circular bases and the rectangular side.
Given:
- Diameter of the cylinder = 3 inches, so the radius \( r = \frac{3}{2} = 1.5 \) inches.
- Height \( h = 2 \) inches.
Calculating the Volume:
- Plug in the values to the volume formula: \[ V = 3.14 \cdot (1.5)^2 \cdot 2 \]
- Calculate \( (1.5)^2 \): \[ (1.5)^2 = 2.25 \]
- Now calculate the volume: \[ V = 3.14 \cdot 2.25 \cdot 2 \]
- Calculate \( 3.14 \cdot 2.25 = 7.065 \).
- Now multiply by 2: \[ V = 7.065 \cdot 2 = 14.13 \]
Rounding to the nearest tenth:
The volume \( V \) is approximately \( 14.1 \) cubic inches.
Calculating the Surface Area:
- Plug the values into the surface area formula: \[ A = 2 \cdot 3.14 \cdot 1.5 \cdot (2 + 1.5) \]
- Calculate \( (2 + 1.5) = 3.5 \).
- Now calculate: \[ A = 2 \cdot 3.14 \cdot 1.5 \cdot 3.5 \]
- First calculate \( 2 \cdot 3.14 \cdot 1.5 = 9.42 \).
- Now multiply that by \( 3.5 \): \[ A = 9.42 \cdot 3.5 = 32.87 \]
Rounding to the nearest tenth:
The surface area \( A \) is approximately \( 32.9 \) square inches.
Final Answers:
- Volume: \( 14.1 \) cubic inches
- Surface Area: \( 32.9 \) square inches