A toy is in the form of a cone mounted on a hemisphere of common base radius $ 7 \mathrm{~cm} $. The total height of the toy is $ 31 \mathrm{~cm} $. Find the total surface area of the toy.

Given: 

A toy is in the form of a cone mounted on a hemisphere of common base radius \( 7 \mathrm{~cm} \). The total height of the toy is \( 31 \mathrm{~cm} \).

To do: Find the total surface area of the toy.

Solution:

Height of the cone, $h = 31-7=24\ cm$

Radius of the cone = Radius of the hemisphere = r = 7 cm

Slant height $l=\sqrt{7^2+24^2}=\sqrt{49+576}=\sqrt{625}=25\ cm$

Total surface area of the toy = Surface area of the cone $+$ CSA of the hemisphere

$=2πr^2+πrl$

$=\frac{22}{7}\times7(2(7)+25)$

$=22\times39$

$=858\ cm^2$

Therefore, the total surface area of the toy is $858 cm^2$.

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Updated on: 10-Oct-2022

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