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MODEL PAPER 4 (STANDARD) — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMODEL PAPER 4 (STANDARD)5 Marks
Question
Rasheed got a playing top $($lattu$)$ as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his 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 $\pi=\frac{22}{7} )$.
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Answer

Surface area to colour $=$ surface area of hemisphere $+$ curved surface area of cone
Diameter of hemisphere $=3.5 \ cm$
So radius of hemispherical portion of the lattu $= r =\frac{3.5}{2} \ cm=1.75$
$r =$ Radius of the concial portion $=\frac{3.5}{2}=1.75$
Height of the conical portion $=$ height of top $-$ radius of hemisphere $=5-1.75=3.25 \ cm$
Let $I$ be the slant height of the conical part.
Then,
$l^2=h^2+r^2$
$l^2=(3.25)^2+(1.75)^2$
$\Rightarrow l^2=10.5625+3.0625$
$\Rightarrow l^2=13.625$
$\Rightarrow l=\sqrt{13.625}$
$\Rightarrow l=3.69$
Let $S$ be the total surface area of the top.
Then,
$S=2 \pi r^2+\pi r l$
$\Rightarrow S=\pi r(2 r+l)$
$\Rightarrow S=\frac{22}{7} \times 1.75(2 \times 1.75+3.7)$
$\quad=5.5(3.5+3.7)$
$=5.5(7.2)$
$=39.6 \ cm^2$

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