Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius .the total height of the toy is 15 5 cm . find the total surgace area of the toy? only right answer can be put in answer key .​

Answer 1

Answer:

rad. of cone=rad. of hemisphere =3.5cm(given)

Also,

ht of toy=15.5cm(given)

ht of hemisphere = 3.5cm

ht of cone = 15.5 - 3.5

=12cm

slant ht. of cone =under root h^2+r^2

=under root (12^2+3.5^2)

= under root 144+12.25

= under root 156.25

12.5cm

CSA of hemisphere = 2×22/7×(3.5)^2

=77cm^2

CSA of cone = 22/7×3.5×12.5

137.5cm^2

TSA of toy=CSA of hemisphere +CSA of cone

77+137.5

= 214.5cm^2

Answer 2

Given :

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius . The total height of the toy is 15.5 cm .

To find :

Find the total surface area of the toy.

Solution :

$\star$ Total surface area of toy = CSA of cone + SA of hemisphere

Total height of toy = 15.5 cm

Radius of cone = 3.5 cm

∴ Height of cone, h = (15.5 - 3.5) = 12 cm

∴ Slant height, l = √(h² + r²)

⇒ l = √{(12² + (3.5)²}

⇒ l = √{144 + 12.25}

⇒ l = √156.25

⇒ l = 12.5 cm

Now. csa of cone :

$\longmapsto\underline{\boxed{\mathfrak{CSA \ of \ cone = \pi rl }}} \\\\\\ \longmapsto\sf CSA \ of \ cone = \dfrac{22}{7} \times (3.5) \times (12.5) \\\\ \\ \longmapsto\underline{\underline{\mathfrak{CSA \ of \ cone = 137.5 \ cm^2 }}} \ \star$

Now, surface area of hemisphere :

$\longmapsto\underline{\boxed{\mathfrak{Surface \ area \ of \ hemisphere = 2 \pi r^2 }}} \\\\\\ \longmapsto\sf Surface \ area \ of \ hemisphere = 2 \times \dfrac{22}{7} \times (3.5)^2 \\\\ \\ \longmapsto\sf Surface \ area \ of \ hemisphere = \dfrac{44}{7} \times 12.25 \\\\ \\ \longmapsto\underline{\underline{\mathfrak{Surface \ area \ of \ hemisphere = 77 \ cm^2 }}} \ \star$

Therefore,

$\longmapsto\sf TSA \ of \ toy = CSA \ of \ cone + Surface \ area \ of \ hemisphere \\\\ \\ \longmapsto\sf TSA \ of \ toy = 137.5 + 77 \\\\ \\ \longmapsto\underline{\underline{\boxed{\mathfrak{TSA \ of \ toy = 214.5 \ cm^2 }}}}\ \star$

$\therefore\underline{\textsf{Total surface area of toy = {\textbf{214.5 cm{ ^{\bf2} }}}}}$