Question

18. A toy is in the form of a cone mounted on a hemisphere of same
radius 7 cm. If thetotal height of the toy is 31 cm, find its total surface
area. (Use T = 227)​

Answer 1

Correct Question :

• A toy is in the form of a cone mounted on a hemisphere of same radius 7 cm. If the height of the toy is 31 cm, find its total surface area area. (Use π = 22/7)

Given :

• Radius of toy = 7cm
• Height of toy = 31 cm

To Find :

• Total surface Area

Solution :

• Radius = 7cm
• Height = (31 - 7) = 24cm

Length of cone :

⟹ Length = √(7)² + (24)²

⟹ Length = √49 + 576

⟹ Length = √625

⟹ Length = 25cm

TSA of cone = 2πr² + πrl

⟹ 2 × 22/7 × (7)² × 22/7 × 7 × 25

⟹ 2 × 22 × 7 + 22 × 25

⟹ 44 × 7 + 550

⟹ 308 + 550

⟹ 858cm²

∴ Total surface area is 858cm²

Answer 2

$\small \: {\underline{\mathrm{Given:}}}$

• Total height of toy = 31 cm.
• Radius of hemisphere, cone = 7 cm.

$\small \: {\underline{\mathrm{To\:find:}}}$

• Total surface area of toy.

$\small \: {\underline{\mathrm{Solution:}}}$

$\mapsto\:\sf \:Height \:of\: toy \:=\: 31\: cm$

$\mapsto\:\sf\:Height \:of \:cone\: = \:(31\:-\:7)\:cm\:=\:24\:cm$

$\mapsto\:\sf\:Slant\:height\:of\:cone\:=\:\sqrt{(7)^2\:+(24)^2}$

$\mapsto\:\sf\:Slant\:height\:of\:cone\:=\:\sqrt{49\:+\:576}$

$\mapsto\:\sf\:Slant\:height\:of\:cone\:=\:\sqrt{625}$

$\mapsto\:\sf\:Slant\:height\:of\:cone\:=\:25\:cm$

$\boxed{\small{\sf\:{TSA \:of \:toy\: =\: CSA (cone)\: +\: CSA (hemisphere)}}}$

➱ TSA of toy = πrl + 2πr²

➱ TSA of toy = πr(l + 2r)

➱ TSA of toy = 22/7 × 7 (25 + 2 × 7)

➱ TSA of toy = 22 (25 + 14)

➱ TSA of toy = 22 × 39

➱ TSA of toy = 858

∴ Total surface area of toy is 858 cm².