Final answer:
The cube with a volume of 500 cm³ has an edge length of approximately 7.937 cm, a surface area of 377.21 cm², and a base perimeter of 31.748 cm. For a cylinder with a volume of 500 cm³ and a height of 10 cm, the radius would be approximately 2.527 cm, a circumference of the base of 15.876 cm, and a surface area of about 398.18 cm².
Step-by-step explanation:
To describe the dimensions of two objects with volumes of about 500 cm³, let's consider a cube and a cylinder.
Cube
For a cube with a volume of 500 cm³:
- The edge length (s) can be found using the volume formula for a cube, V = s³, so s = ∓(500 cm³) which is approximately 7.937 cm.
- The surface area (SA) is 6s², which gives us SA = 6(7.937 cm)² ≈ 377.21 cm².
- The perimeter of the base is 4s, which provides a perimeter of 4(7.937 cm) ≈ 31.748 cm.
Cylinder
For a cylinder with a volume of 500 cm³:
- Assuming we don't know the height (h), we can't find the exact dimensions, but the volume formula for a cylinder is V = πr²h.
- If we assume a height, for example, h = 10 cm, then the radius (r) can be found by rearranging the volume formula to r = ∓(V/πh); if V = 500 cm³ and h = 10 cm, then r ≈ 2.527 cm.
- The circumference of the base is 2πr, which would be ≈ 15.876 cm.
- The surface area (SA) is 2πrh + 2πr², adding the side and two base areas; using the previous values for r and h, SA ≈ 398.18 cm².