A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use \(\pi=\frac{22 }{7}\)
It can be observed that Radius (r) of cylindrical part = Radius (r) of hemispherical part \(=\frac{\text{Distance}\ \text{ of}\ \text{ the }\ \text{capsule}}{2}=\frac{5}{2}\)
Length of cylindrical part (h) = Length of the entire capsule \(β 2 Γ r = 14 β 5 = 9\) cm
Surface area of capsule \(= 2Γ\)CSA of hemispherical part + CSA of cylindrical part \(= 2Γ2\pi r^2 +2\pi rh\)
Surface area and volume are two important concepts in geometry that are used to measure the size and shape of three-dimensional objects.
Surface area is the measure of the total area that the surface of an object covers. It is expressed in square units, such as square meters or square inches. To calculate the surface area of an object, we find the area of each face or surface and add them together. For example, the surface area of a cube is equal to six times the area of one of its faces.
Volume, on the other hand, is the measure of the amount of space that an object takes up. It is expressed in cubic units, such as cubic meters or cubic feet. To calculate the volume of an object, we measure the length, width, and height of the object and multiply these three dimensions together. For example, the volume of a cube is equal to the length of one of its edges cubed.
Surface area and volume are important in many fields, such as architecture, engineering, and manufacturing. For example, surface area is used to calculate the amount of material needed to cover an object, while volume is used to determine the amount of space that a container can hold. Understanding surface area and volume is also important in calculus and physics, where they are used to model the behavior of objects in three-dimensional space.
