Question

A toy is in the form of cone of radius 3.5cm mounted on a hemisphere of same radius. Total height of the toy is 15.5cm. Find total surface area of toy [use pi = 22/7]

Answer 1

Question:

A toy in the form of cone of radius 3.5cm mounted on a hemisphere of same radius. Total height of the toy is 15.5cm. Find the total surface area of toy?

Answer:

214.5cm²

Step-by-step explanation:

It can be observed that the radius of the conical part and the hemisphere part is same (3.5cm)

Height of the hemisphere part=3.5=7/2cm

Height of the conical part=15.5-3.5=12cm

Slant height of conical part=√r²+h²

⇒$\sqrt{(\frac{7}{2})^{2}+(12)^{2}}$

⇒$\sqrt{\frac{49}{4}+144}$

⇒$\sqrt{\frac{49+576}{4}}$

⇒$\sqrt{\frac{625}{4}}$

⇒$\frac{25}{2}$

Total surface area of toy=CSA of conical part+CSA of hemispherical part=πrl+2πr²

⇒$\pi rl+2\pi r^{2}$

⇒$\frac{22}{7}×\frac{7}{2}×\frac{25}{2}+2×\frac{22}{7}×\frac{7}{2}×\frac{7}{2}$

⇒137.5×77

⇒214.5cm²

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Therefore, Total surface area of toy = 214.5cm²