To determine the volume and surface area of the figure in question, we need to clarify what the figure is. Given the dimensions of 3 inches and 9 inches, it seems likely that we are dealing with a cylinder.
Volume of a Cylinder
The formula for the volume \( V \) of a cylinder is given by: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
Surface Area of a Cylinder
The formula for the surface area \( SA \) of a cylinder is given by: \[ SA = 2\pi r(h + r) \]
Let’s assume the height is 9 inches and the diameter is 3 inches, which gives a radius of \( r = \frac{3}{2} = 1.5 \) inches.
Calculating Volume
- Substitute the values into the volume formula: \[ V = \pi (1.5)^2 (9) \] \[ V = 3.14 \times (2.25) \times 9 \] \[ V = 3.14 \times 20.25 \] \[ V \approx 63.6 \text{ in}^3 \]
Calculating Surface Area
- Substitute the values into the surface area formula: \[ SA = 2\pi (1.5)(9 + 1.5) \] \[ SA = 2 \times 3.14 \times 1.5 \times 10.5 \] \[ SA = 2 \times 3.14 \times 15.75 \] \[ SA \approx 99.9 \text{ in}^2 \]
Final Comparison
Let's compare these results with the provided options:
- A: V = 84.8 in³ SA = 565.2 in²
- B: V = 1,017.4 in³ SA = 395.6 in²
- C: V = 169.6 in³ SA = 113 in²
- D: V = 254.3 in³ SA = 226.1 in²
Since the calculations for both the volume (approximately 63.6 in³) and surface area (approximately 99.9 in²) do not match any option exactly, it's possible that the dimensions provided relate to a different figure, or there may be an error. Please ensure the dimensions given represent a cylinder as described or clarify the shape for a more accurate calculation.