Question

A toy is in the form of 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 surface area of the toy.​

Answer 1

$\large{\underline{\rm{\green{\bf{Question:-}}}}}$

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 surface area of the toy.

$\large{\underline{\rm{\green{\bf{Given:-}}}}}$

The radius of the cone = 3.5 cm

Total height of the toy = 15.5 cm

$\large{\underline{\rm{\green{\bf{To \: Find:-}}}}}$

The total surface area of the toy.

$\large{\underline{\rm{\green{\bf{Solution:-}}}}}$

Given that, the radius of the cone and the hemisphere (r) = 3.5 cm or 7/2 cm

The total height of the toy =  15.5 cm.

So, the height of the cone (h) = $\sf 15.5-3.5 = 12 \: cm$

According to the question,

Slant height of the cone (h) = $\sf \sqrt{h^{2}+r^{2}}$

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

$\implies \sf l=\sqrt{12^{2}+\bigg(\dfrac{7}{2} \bigg)^{2} }$

$\implies \sf l=\sqrt{144+\dfrac{49}{4} }$

$\sf =\sqrt{ \dfrac{(576+49)}{4} }$

$\sf =\sqrt{\dfrac{625}{4} }$

∴ The curved surface area of cone = $\sf \pi r l$

Substituting the values, we get

$\sf \dfrac{22}{7} \times \dfrac{7}{2} \times \dfrac{25}{2} =\dfrac{275}{2} \: cm^{2}$

Also, the curved surface area of the hemisphere = $\sf 2 \pi r^{2}$

Substituting their values,

$\sf 2 \times \dfrac{22}{7}\times \dfrac{7}{2} ^{2}$

$\sf =77 \: cm^{2}$

Now, the Total surface area of the toy = CSA of cone + CSA of hemisphere

$\implies \sf \dfrac{275}{2} +77 \: cm^{2}$

$\implies \sf \dfrac{(275+154)}{2} \: cm^{2}$

$\implies \sf \dfrac{429}{2} \: cm^{2} =214.5 \: cm^{2}$

So, the total surface area (TSA) of the toy is 214.5 cm²

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

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