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