Find the volume and surface area of a regulation cricket ball (radius ~3.6 cm).
Every 3D solid has a volume (how much space it fills or holds) and a surface area (how much material it would take to cover its outside). This tool covers the six shapes taught in most school geometry courses — cube, cuboid, sphere, hemisphere, cylinder, and cone — and draws a labeled diagram of whichever one you pick.
For the curved shapes (hemisphere, cylinder, cone), the tool shows both the <strong>curved surface area</strong> (just the curved part) and the <strong>total surface area</strong> (curved part plus the flat circular base or bases) — a distinction that trips a lot of people up, since which one a problem is actually asking for changes the answer completely.
Curved surface area (CSA) is just the curved part — the outside of a cylinder’s tube, not its lids. Total surface area (TSA) adds the flat circular base(s) on top. A cube and cuboid don’t have this distinction since all their faces are flat, so only one surface area is shown for those two.
Volume is simply half of a full sphere’s volume. But surface area isn’t just half a sphere’s surface area — slicing a sphere in half removes the curved surface on that cut face and replaces it with a new flat circular face, so the curved surface area is exactly half a sphere’s (2πr²), while the total surface area adds that new flat circle back in (3πr² total).
It’s the straight-line distance from the tip of the cone to the edge of its base circle — not the same as the cone’s vertical height. By the Pythagorean theorem, slant height = √(radius² + height²), since the radius, the height, and the slant form a right triangle.