Question

Two cones of identical dimensions with, base radius 8 units and height 15 units are joined at their bases. What will be the surface area of the new shape (in sq units)?

Answer 1

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


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

As the radii of the cones are placed side by side, we will not consider the circular areas of their bases.

Surface area of the shape so formed
= Curved surface area of first cone + Curved surface area of second cone
= 2 × (Surface area of cone) [Since, both cones are identical]
$=2\times \pi rl...\text{where l is the slant height}$
$\text{of the cone}$

$=2\times \pi \times r\times \sqrt{r^2+h^2}(\because l=\sqrt{r^2+h^2})$

On putting the values, we get:
$=2\times \frac{22}{7}\times 8\times \sqrt{(8{)}^2+(15{)}^2}$

$=\frac{2\times 22\times 8\times \sqrt{64+225}}{7}$

$=\frac{44\times 8\times \sqrt{289}}{7}$

$=\frac{5984}{7}$

$=854.85\text{sq units}$

$\approx 855\text{sq units}$

Hence , the surface area of shape so formed is 855 sq units.