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.

Answer 1

According to the question,

We get the figure given below,

We know that,

Total surface area of shape formed = Curved area of first cone + Curved surface area of second cone

Since, both cones are identical,

We have,

Total surface area of shape formed = Curved area of first cone + Curved surface area of the second cone

= 2(Surface area of cone)

We also know that,

Surface area of cone = πrl, where r = radius and l = slant height

And the total surface area of shape so formed = 2πrl

Given in the question that,

Radius, r = 8 cm

Height, h = 15 cm

Therefore,

Area = Curved area of first cone + Curved surface area of the second cone

= 2(Surface area of the cone)

= 2 × πrl

= `2 xx π xx "r" xx sqrt("r"^2 + "h"^2)`

= `2 xx 22/7 xx 8 xx sqrt(8^2 + 15^2)`

= `50.28 xx sqrt(289)`

= 854.85 cm²

= 855 cm²  ...(Approx)

Hence, the surface area of shape so formed is 855cm².