Question

a toy is in the form of a cone mounted on a hemisphere of radius 3.5 CM the total height of the toys 15.5 cm find the TSA and volume of the toy ​

Answer 1

$\bf\huge\blue{\underline{\underline{ Question : }}}$

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 CM the total height of the toy 15.5 cm find the TSA and volume of the toy.

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• A toy is in the form of a cone mounted on a hemisphere.

• Radius(r) of cone = hemisphere = 3.5 cm.

• Total Height(h) of the toy = 15.5 cm.

★ To find,

• Total Surface Area of the you.

★ Formula :

◼ For finding the total surface area of the toy, we have to apply a suitable formula.

◼ This formula is applicable for any solids like :

• Cone - Hemisphere solids.
• Cylinder - Hemisphere solids.
• Cube - Cuboid solids.
• Cone - Cylinder - Hemisphere solids etc.

$\boxed{\rm{\red{ Total\:Surface\:Area\:of\:Toy = Curved\:Surface\:Area\:of\:Cone - Curved\:Surface\:Area\:of\: Hemisphere }}}$

➡ ᴄᴀsᴇ - 1 :-

$\tt \rightarrow Curved \:Surface\: Area\: of\: Cone= \pi rl$

• π = 22/7
• r = 3.5 cm.
• l = ?

$\tt \rightarrow Slant \:Height(l)= \sqrt{h^{2} + r^{2}}$

• r = 3.5 cm.
• h = ?

✒ Height of Cone = Height of Toy - Radius of base.

↪ 15.5 - 3.5

↪ 12 cm.

∴ Height of Cone = 12 cm.

• Substitute value of height in Slant Height formula.

$\sf \leadsto l = \sqrt{(12)^{2} + (3.5)^{2}}$

$\sf \leadsto l = \sqrt{144 + 12.5}$

$\sf \leadsto l = \sqrt{156 .25}$

$\sf \leadsto l = 12.5$

∴ Hence, Slant Height = 12.5 cm.

• Now substitute value of l in formula.

$\sf \implies \cfrac{22}{7} \times 3.5 \times 12.5$

$\sf \implies \cancel{\cfrac{22}{7}} \times \cancel{\cfrac{35}{10}}\times \cancel{\cfrac{125}{10}}$

$\sf \implies \cfrac{275}{2}$

$\sf \implies 137.5$

∴ CSA of Cone = 137.5 cm².

➡ ᴄᴀsᴇ - 2 :-

$\tt \rightarrow Curved \:Surface\: Area\: of\:Hemisphere= 2 \pi r^{2}$

• π = 22/7
• r = 3.5 cm.

$\sf \implies 2 \times \cfrac{22}{7} \times 3.5 \times 3.5$

$\sf \implies \cancel{2} \times \cancel{\cfrac{22}{7}}\times \cancel{\cfrac{35}{10}} \times \cancel{\cfrac{35}{10}}$

$\sf \implies 77$

∴ CSA of Hemisphere = 77 cm².

★ Now,

We can find out the value of TSA of Toy.

$\sf \implies TSA = 137.5 + 77$

$\sf \implies TSA = 214.5$

$\underline{\boxed{\rm{\purple{\therefore Hence,\:The\:Total\:Surface\:Area\:of\:Toy=214.5\:cm^{2}.}}}}\:\orange{\bigstar}$

______________________________________________________

Answer 2

Answer:

We have,

Radius of cone = Radius of hemisphere = 3.5 cm.

Height of the toy = 15.5 cm

To calculate the CSA of cone we have to find first the Slant Height of the cone :]

Slant Height = h² + r²

Slant Height = (15.5)² + (3.5)²

Slant Height = 12.25 + 144

Slant Height = 156.25 cm²

Slant Height = 12.5 cm

Now, we will calculate the TSA of the toy :

➳ TSA of toy = CSA of hemisphere + CSA of cone

➳ TSA of toy = 2πr² + πrl

➳ TSA of toy = 2π(3.5)² + π(3.5)(12.5)

➳ TSA of toy = 24.5π + 43.75π

➳ TSA of toy = 68.25π

➳ TSA of toy = 68.25 * 22/7

➳ TSA of toy = 214.5 cm²