Question

Find respectively the surface area(in $m{m}^2$) and volume(in $m{m}^3$) of the capsule shown in the figure given below:

• A. $72\pi \&90\pi$
• B. $90\pi \&72\pi$
• C. $36\pi \&54\pi$

Answer 1

The correct option is A $72\pi \&90\pi$

Surface Area of the Capsule = Curved Surface Area(CSA) of the cylinder + 2(Curved Surface Area(CSA) of the hemisphere)

Curved Surface Area(CSA) of the cylinder $=2\pi rh$
Curved Surface Area(CSA) of the cylinder $=2\pi \left(3\right)\left(6\right)$
Curved Surface Area(CSA) of the cylinder $=36\pi m{m}^2$

Curved Surface Area(CSA) of the hemisphere $=\frac{1}{2}\times$ Surface Area of the Sphere
Curved Surface Area(CSA) of the hemisphere $=\frac{1}{2}\times 4\pi r^2$
Curved Surface Area(CSA) of the hemisphere $=2\pi r^2$
Curved Surface Area(CSA) of the hemisphere $=2\pi (3{)}^2$
Curved Surface Area(CSA) of the hemisphere $=18\pi m{m}^2$


Surface Area of the Capsule $=36\pi +2\left(18\pi \right)$
Surface Area of the Capsule $=36\pi +36\pi$
Surface Area of the Capsule $=72\pi m{m}^2$


Volume of the Capsule = Volume of the Cylinder + Volume of both the hemispheres
Volume of the Cylinder $=\pi r^{2}h$
Volume of the Cylinder $=\pi \left(3{)}^2\right(6)$
Volume of the Cylinder $=54\pi m{m}^3$

Volume of both the hemispheres $=2\left(\frac{1}{2}Volumeofthesphere\right)$
Volume of both the hemispheres $=2(\frac{1}{2}\times \frac{4}{3}\pi r^3)$
Volume of both the hemispheres $=\frac{4}{3}\pi (3{)}^3$
Volume of both the hemispheres $=36\pi m{m}^3$

Volume of the Capsule $=54\pi +36\pi$
Volume of the Capsule $=90\pi m{m}^3$