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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 $858 cm^2$.