Question

Jackson got a capsule shaped object. The dimensions of this object are represented as follows:


What will be the surface area of this object?

• A. $32\pi {\text{cm}}^2$
• B. $40\pi {\text{cm}}^2$
• C. $48\pi {\text{cm}}^2$
• D. $36\pi {\text{cm}}^2$

Answer 1

The correct option is C $48\pi {\text{cm}}^2$

Observe the given figure, it consists of a cylinder and two hemispheres on the sides. These figures can be separately represented as,



The surface area of the given object can be calculated as follows,

$\text{Required Surface Area}=\text{Curved surface area of cylinder}+2\text{Curved surface area of hemisphere}$

First, lets find the surface area of cylinder. It can be observed that the radius of cylinder is $2\text{cm}$ and its height $8\text{cm}$, therefore its curved surface area will be,

$\begin{array}{cc}\text{Curved surface area of cylinder}& =2\pi rh\\ & =2\pi \left(2\right)\left(8\right)\\ & =32\pi \end{array}$

Now, the curved surface area of hemisphere with radius $2\text{cm}$ is calculated as,

$\begin{array}{cc}\text{Curved surface area of hemisphere}& =\frac{1}{2}\times \text{Surface area of sphere}\\ & =\frac{1}{2}\times 4\pi r^2\\ & =2\pi r^2\\ & =2\pi \left(2^2\right)\\ & =8\pi \end{array}$

Substitute the value of curved surface area of cylinder and hemisphere in the equation for required surface area,

$\begin{array}{cc}\text{Required Surface Area}& =32\pi +2\left(8\pi \right)\\ & =32\pi +16\pi \\ & =48\pi \end{array}$

Thus, the surface area of given capsule shaped object is $48\pi {\text{cm}}^2$.