Question

A toy is in the form of a cone of radius 2 cm mounted on another inverted cone of same radius and same depth. Find the TSA of the toy if the height of cone is 4 cm.

• A. $4\pi \sqrt{5}c{m}^2$
• B. $8\pi \sqrt{5}c{m}^2$
• C. $2\pi \sqrt{5}c{m}^2$
• D. $4\pi \sqrt{10}c{m}^2$

Answer 1

The correct option is B $8\pi \sqrt{5}c{m}^2$

Lets draw the toy as mentioned in question with given dimesnions.
Let's assume the slant height of both the cone to be l.
TSA of toy = CSA of upper cone + CSA of bottom cone
As all the dimensions of both the cone are equal,
CSA of upper cone = CSA of bottom cone

Hence, TSA of toy = 2 x CSA of upper cone

$\to$CSA of upper cone
For the upper cone given in the figure,
Radius $=r=2$ cm and height $=h=4$ cm.
Slant height $=l=\sqrt{r^2+h^2}$
Slant height $=l=\sqrt{2^2+4^2}$
$=\sqrt{20}$
$=\sqrt{20}cm$

Curved Surface Area(CSA) $=\pi rl$
Curved Surface Area(CSA) $=\pi \times 2\times \sqrt{20}=\pi \times 2\times \sqrt{2\times 2\times 5}=\pi \times 4\times \sqrt{5}$
Curved Surface Area(CSA) $=4\pi \sqrt{5}c{m}^2$

TSA of toy = 2 x CSA of upper cone
$=2\times 4\pi \sqrt{5}c{m}^2=8\pi \sqrt{5}c{m}^2$