Mathematics
Mathematics
Problem
A cylindrical tank has radius 0.5 m and length 2 m. Each end of the cylinder is closed by a hemispherical cap of the same radius. Calculate the outer surface area of the tank. (Use .)Intuitive explanation
This problem combines two shapes: a cylinder and two hemispheres. The key insight is recognizing that the two hemispherical caps together form a complete sphere, so you can use the sphere's surface area formula rather than calculating each cap separately. Find the curved surface area of the cylinder, add it to the surface area of one complete sphere, and you'll have the total outer surface.
Intuitive explanation
This problem combines two shapes: a cylinder and two hemispheres. The key insight is recognizing that the two hemispherical caps together form a complete sphere, so you can use the sphere's surface area formula rather than calculating each cap separately. Find the curved surface area of the cylinder, add it to the surface area of one complete sphere, and you'll have the total outer surface.