To find the volume and surface area of a solid figure, we need to determine what specific solid shape is being described. Given the dimensions \(3\), \(6\), and \(10\), it sounds like you're describing a rectangular prism or possibly a cylinder.
Case 1: Rectangular Prism
If the dimensions \(3\), \(6\), and \(10\) are the lengths of the sides of a rectangular prism, we can calculate the volume \(V\) and the surface area \(SA\) as follows:
-
Volume:
\[ V = l \cdot w \cdot h \]
Where \( l = 3 \), \( w = 6 \), \( h = 10 \).
\[ V = 3 \cdot 6 \cdot 10 = 180 \text{ cubic feet} \] -
Surface Area:
\[ SA = 2(lw + lh + wh) \]
\[ SA = 2(3 \cdot 6 + 3 \cdot 10 + 6 \cdot 10) \]
\[ SA = 2(18 + 30 + 60) = 2(108) = 216 \text{ square feet} \]
Case 2: Cylinder
If the dimensions \(3\) and \(6\) are the radius and height of a cylinder:
Assuming \(radius = 3\) and \(height = 6\):
-
Volume:
\[ V = \pi r^2 h \]
\[ V = 3.14 \cdot (3^2) \cdot 6 \]
\[ V = 3.14 \cdot 9 \cdot 6 = 3.14 \cdot 54 = 169.56 \text{ cubic feet} \] -
Surface Area:
\[ SA = 2\pi r(h + r) \]
\[ SA = 2 \cdot 3.14 \cdot 3 \cdot (6 + 3) = 2 \cdot 3.14 \cdot 3 \cdot 9 = 169.56 \text{ square feet} \]
Based on our calculations:
- For Rectangular Prism:
- Volume = \(180 \text{ ft}^3\)
- Surface Area = \(216 \text{ ft}^2\)
Thus, the answer that fits is: A. V = 180 ft cubed; SA = 216 ft squared.
If my assumptions about the figure are incorrect, please provide detailed information regarding the shape, and I can adjust the calculations.