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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 3 · Set 1 · Q14
John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by themselves and to buy a cake from a…
John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by themselves and to buy a cake from a bakery shop. For these two items, they decided the following dimensions : Cake : Cylindrical shape with diameter $\displaystyle 24$ cm and height $\displaystyle 14$ cm. Cap : Conical shape with base circumference $\displaystyle 44$ cm and height $\displaystyle 24$ cm.
Based on the above information, answer the following questions :
(a)
How many square cm paper would be used to make $\displaystyle 4$ such caps ?
(b)
The bakery shop sells cakes by weight ($\displaystyle 0$•$\displaystyle 5$ kg, $\displaystyle 1$ kg, $\displaystyle 1$•$\displaystyle 5$ kg, etc.). To have the required dimensions, how much cake should they order, if $\displaystyle 650 \mathrm{~cm}^{3}$ equals $\displaystyle 100$ g of cake ?
Marking-scheme solution
(a)
$\displaystyle 2 \pi r=44$
$\displaystyle \Rightarrow r=7$
Therefore, $\displaystyle l=\sqrt{24^{2}+7^{2}}=25 \mathrm{~cm}$
Paper required for $\displaystyle 4$ caps $\displaystyle =4 \times \pi r l$
\[\begin{array}{l}
=4 \times \frac{22}{7} \times 7 \times 25 \\
=2200 \mathrm{~cm}^{2} \text { or } 700 \pi \mathrm{~cm}^{2}
\end{array}
\]
(b)
Volume of cake $\displaystyle =\frac{22}{7} \times 12 \times 12 \times 14$
\[=6336 \mathrm{~cm}^{3}
\]
$\displaystyle 6336 \mathrm{~cm}^{3}$ is nearest to $\displaystyle 6500 \mathrm{~cm}^{3}$
Now, $\displaystyle 650 \mathrm{~cm}^{3}=100 \mathrm{~g}$
\[\Rightarrow 6500 \mathrm{~cm}^{3}=1 \mathrm{~kg}
\]
$\displaystyle \therefore 1 \mathrm{~kg}$ cake should be ordered.
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.