Final answer:
The surface area of the volume of the cylinder carved out from a cubical piece is 2.3562 cm².
Step-by-step explanation:
To find the surface area of the volume of a cylinder carved out of a cubical piece of body, we need to know the diameter of the sphere being carved out. Assuming the diameter of the sphere is equal to the side length of the cube, which is 1 cm, we can proceed with the calculation. The surface area of a cube is given by the formula SA = 6s², where s is the side length. So, the surface area of the cube is 6 × (1 cm)² = 6 cm². Now, let's find the volume of the cylinder. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since the diameter of the sphere is equal to the side length of the cube, the radius of the cylinder is half of that, which is 0.5 cm. Let's assume the height of the cylinder is also 0.5 cm for simplicity. So, the volume of the cylinder is V = π(0.5 cm)²(0.5 cm) = 0.3927 cm³. Finally, let's find the surface area of the cylinder. The surface area of a cylinder is given by the formula SA = 2πrh + 2πr². Plugging in the values, we get SA = 2π(0.5 cm)(0.5 cm) + 2π(0.5 cm)² = 1.5708 cm² + 0.7854 cm² = 2.3562 cm². Therefore, the surface area of the volume of the cylinder is 2.3562 cm².
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