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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 2 · Set 1 · Q36
In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made…
In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is ₹ $\displaystyle 20$ per $\displaystyle \mathrm{cm}^{2}$.
Based on the above, answer the following questions :
(i)
What is the area of the quadrant ODCO ?
(ii)
Find the area of $\displaystyle \Delta \mathrm{AOB}$.
(iii)
(a)
What is the total cost of silver plating the shaded part ABCD ?
OR
(b)
What is the length of arc CD ?
Marking-scheme solution
(i)
Area of sector ODCO \(\displaystyle =\frac{22}{7} \times 7 \times 7 \times \frac{90}{360}=\frac{77}{2}\) or $\displaystyle 38.5$
∴ Area of sector ODCO is \(\displaystyle \frac{77}{2}\) or \(\displaystyle 38.5 \mathrm{~cm}^{2}\)
\[\text { (ii) } \operatorname{ar}(\Delta \mathrm{AOB})=\frac{1}{2} \times 10 \times 10=50
\]
\(\displaystyle \therefore \operatorname{ar}(\Delta \mathrm{AOB})\) is \(\displaystyle 50 \mathrm{~cm}^{2}\)
(iii) (a) Required cost \(\displaystyle =(50-38 \cdot 5) \times 20\)
\[\text { = } 230
\]
∴ required cost is ₹ 230.
OR
\[\text { (iii) (b) Length of arc } \begin{aligned}
\mathrm{CD} & =\frac{90}{360} \times 2 \times \frac{22}{7} \times 7 \\
& =11
\end{aligned}
\]
∴ Length of arc CD is $\displaystyle 11$ cm.
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