Question

A table lamp is in the shape of the frustum of a right circular cone whose curved area is $1200\text{ }{{\text{m}}^{2}}$ and the area of the base and top is $2400\text{ }{{\text{m}}^{2}}$ . Find the total surface area of the frustum cone.
(a) $1600\text{ }{{\text{m}}^{2}}$
(b) $2600\text{ }{{\text{m}}^{2}}$
(c) $3600\text{ }{{\text{m}}^{2}}$
(d) $4600\text{ }{{\text{m}}^{2}}$

Answer 1

Hint: We know that the total surface area of a three dimensional figure is the sum of its lateral surface area added with the area of the base and the top, if applicable. So, to solve the above question, just add the two areas given in the questions and report the answer.

Complete step by step solution:
Let us start the solution to the above question by drawing a diagram of the situation given in the question.

So, the coloured part of the figure represents the curved surface area, while the two circles at the end represents the top and bottom of the frustum cone.
 Now, we know that the total surface area of a three dimensional figure is the sum of its lateral surface area added with the area of the base and the top, if applicable. So, for the frustum cone, the curved surface area given to us is 1200 sq meters and the area of the top and bottom surface together is 2400 sq meters. SO, to get the total surface area of the frustum cone, we will add the two. On doing so, we get
 Total area of the frustum cone = 1200+2400 = 3600 sq meters.
Hence, the answer to the above question is option (c).

Note: It is important that you remember the formulas related to the total surface area of the frustum and other three dimensional figures as they are used very often. The formula for TSA of a frustum cone is $\pi \left( {{r}_{1}}^{2}+{{r}_{2}}^{2}+\left( {{r}_{1}}+{{r}_{2}} \right)\sqrt{{{h}^{2}}+{{\left( {{r}_{1}}-{{r}_{2}} \right)}^{2}}} \right)$ . Be careful about the calculation part as well, as the only place to make an error in the above question is in the calculation part.