Question

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
[3 marks]

Answer 1

If two cones with same base and height are joined together along their bases, then the shape so formed looks like the figure shown below.

Given:
Radius of cone, r = 8 cm and
Height of cone, h = 15 cm

So, surface area of the shape so formed
= Curved area of first cone + Curved surface area of second cone
= 2.(Surface area of cone) [Since both cones are identical]
[1 mark]

$=2\times \pi rl=2\times \pi \times r\times \sqrt{r^2+h^2}(l=\sqrt{r^2+h^2})=2\times \frac{22}{7}\times 8\times \sqrt{(8{)}^2+(15{)}^2}=\frac{2\times 22\times 8\times \sqrt{64+225}}{7}=\frac{44\times 8\times \sqrt{289}}{7}=\frac{5984}{7}=854.85c{m}^2=855c{m}^2\left(approx\right)$
Hence, the surface area of the shape so formed is $855c{m}^2$.
[2 marks]