Calculate the total surface area of the given combined solid object.

Given,

In a combined solid of a cone and hemisphere,

Height of the cone (h) = 24cm

and diameter of the circular base (d) = 14cm

To find, Total surface area of the solid (TSA)

Here,

The radius of the base (r) = 7cm

and slant height of the cone = \(\sqrt{r^2+h^2}\)

= \(\sqrt{(7)^2+(24)^2}\)

= \(\sqrt{49cm^2+576cm^2}\)

= \(\sqrt{625cm^2}\)

= 25 cm

Now by formula,

C.S.A of a conical part = Πrl

=\(\frac{22}7\times7cm\times25cm\)

= 550cm² 

and C.S.A of hemispherical part = 2Πr² 

= \(2\times\frac{22}7\times(7cm)^2\)

= \(\frac{44}7\times49\)

= 308cm² 

Therefore, the total surface area of the combined solid = C.S.A of conical part + C.S.A of hemispherical; part

= 550cm² + 308cm² 

= 858cm²