Rasheed got a playing top as his birthday present , which surprisingly had no colour on it He - Maths - Surface Areas and Volumes

Question

Rasheed got a playing top as his birthday present , which
surprisingly had no colour on it He wanted to colour it with
crayons The top is shaped like a cone surmounted by a hemisphere
The entire top is 5 cm in height and the diameter of the top is 3 5
cm Find the area he has to colour ( take pie = 22 / 7 )

Rayya Halim · Accepted Answer

total surface area(TSA) of the top = curved surface area(CSA) of hemisphere + curved surface area (CSA) of cone

Now

CSA of hemisphere= $2 Π r^{2} = 2 \times \frac{22}{7} \times {(\frac{3.5}{2})}^{2}$

Now height of cone=height of top - radius of hemisphere

=( 5 - (3.5/2) ) = 3.25 cm

slant height of the cone, l = $\sqrt{r^{2} + h^{2}} = \sqrt{{(\frac{3.5}{2})}^{2} + {(3.25)}^{2}} = 3.7 c m$

CSA of cone= $Π r l = (\frac{22}{7} \times \frac{3.5}{2} \times 3.7) {c m}^{2}$

∴ TSA of top=

$(2 \times \frac{22}{7} \times \frac{3.5}{2} \times \frac{3.5}{2}) + (\frac{22}{7} \times \frac{3.5}{2} \times 3.7) = \frac{22}{7} \times \frac{3.5}{2} (3.5 + 3.7) = 39.6 {c m}^{2}$

1