\(\pi rl+\pi { r }^{ 2 }\quad or\quad \pi r(l+r)\)

piece cut off

Cone and hemisphere.

7 cm

14 cm

\(2\pi r(2r+h)\)

\(\left( \frac { 2r }{ 3 } +h \right) \)

\(\because\) Whole surface of each part=\(=2\pi { r }^{ 2 }+\pi { r }^{ 2 }=3\pi { r }^{ 2 }\)
\(\therefore\) Total surface of two parts=\(=3\pi { r }^{ 2 }+3\pi { r }^{ 2 }=6\pi { r }^{ 2 }\)

\(\frac { Volume \ of \ { 1 }^{ st } \ sphere }{ Volume \ of \ { 11 }^{ nd } \ sphere } =\frac { \frac { 4 }{ 3 } \pi { r }_{ 1 }^{ 3 } }{ \frac { 4 }{ 3 } \pi { r }_{ 2 }^{ 3 } } =\frac { 64 }{ 27 } \)
\(\therefore \ =\frac { { r }_{ 1 }^{ 3 } }{ { r }_{ 2 }^{ 3 } } =\frac { 64 }{ 27 } \)
\(=\frac { { r }_{ 1 } }{ { r }_{ 2 } } =\frac { 4 }{ 3 } \)
Ratio of their surface areas=\(\frac { Surface \ are \ of \ { I }^{ st } \ sphere }{ Surface \ are \ of \ { II }^{ nd } \ sphere } \)
\(=\frac { 4\pi { r }_{ 1 }^{ 2 } }{ 4\pi { r }_{ 2 }^{ 2 } } ={ \left( \frac { { r }_{ 1 } }{ { r }_{ 2 } } \right) }^{ 2 }\)
\(={ \left( \frac { 4 }{ 3 } \right) }^{ 2 }=\frac { 16 }{ 9 } \)
=16:9

Volume of upper cone\(=\frac { 1 }{ 3 } \pi { \left( \frac { r }{ 2 } \right) }^{ 2 }\times \frac { h }{ 2 } \)
\(=\frac { 1 }{ 3 } \pi \frac { { r }^{ 2 } }{ 2 } \times \frac { h }{ 2 } \)
\(=\frac { 1 }{ 3 } \pi \frac { { r }^{ 2 }h }{ 2 } \)
Volume of cone\(=\frac { 1 }{ 3 } \pi { r }^{ 2 }h\)
\(\frac { Volume \ of \ upper \ part \ of \ cone }{ Volume \ of \ cone } =\frac { \frac { 1 }{ 3 } \pi \frac { { r }^{ 2 }h }{ 2 } }{ \frac { 1 }{ 3 } \pi { r }^{ 2 }h } \)
\(=\frac { 1 }{ 8 } \)
= 1:8

Surface area=154 cm²
\(\Rightarrow\ \ 4\pi r^2=154\ \ \Rightarrow r^2={154\times7\over4\times22}\)
\(\Rightarrow\ \ r=\sqrt{7\times7\over2\times2}={7\over2}=3.5\)

False.

Total surface area of the figure = \(\frac { 2\pi { r }h+\pi { r }^{ 2 } }{ upper\quad cylinder } +\frac { \pi { r }^{ 2 }+2\pi { r }h }{ lower\quad cylinder } =4\pi { r }h+2\pi { r }^{ 2 }\) 

Radius of cylinder=radius of cone=radius of hemisphere

Total height of the toy = 30 cm 
height of cone =30 cm-(height of cylinder + r of hemisphere) 
= 30 cm - (13+5) cm =12 cm
l of cone=\(\sqrt { { r }^{ 2 }+{ h }^{ 2 } } =\sqrt { { 12 }^{ 2 }+{ 5 }^{ 2 } } \)
\(=\sqrt { 144+25 } =\sqrt { 169 } =13cm\)
C.S.A. of toy = C.S.A of cone + C.S.A of cylinder + C.S.A. of hemisphere
\(=\pi rl+2\pi rh+{ 2\pi r }^{ 2 }=\pi r(l+2h+2r)\)
\(=\frac { 22 }{ 7 } \times 5(13+2\times 13+2\times 5)\)
\(=\frac { 22 }{ 7 } \times 5(13+26+10)=770{ cm }^{ 2 }\)