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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 2 · Set 1 · Q37
In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is…
In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter $\displaystyle 7$ cm and height $\displaystyle 14$ cm and the other is hemispherical with diameter $\displaystyle 21$ cm.
Based on the above, answer the following questions :
(i)
Find the area of the base of the cylindrical cup.
(ii)
(a)
What is the capacity of the hemispherical cup ?
OR
(b)
Find the capacity of the cylindrical cup.
(iii)
What is the curved surface area of the cylindrical cup ?
Marking-scheme solution
(i)
Area of base of the cylindrical cup $\displaystyle =\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}=\frac{77}{2}$ or $\displaystyle 38.5$
∴ Area of base of the cylindrical cup is $\displaystyle \frac{77}{2}$ or $\displaystyle 38.5 \mathrm{~cm}^{2}$
(ii)
(a)
Capacity of hemispherical cup $\displaystyle =\frac{2}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}$
\[=\frac{4851}{2} \text { or } 2425.5
\]
∴ Capacity of hemispherical cup is $\displaystyle \frac{4851}{2} \mathrm{~cm}^{3}$ or $\displaystyle 2425.5 \mathrm{~cm}^{3}$
OR
(b)
Capacity of cylindrical cup $\displaystyle =\frac{22}{7} \times(7)^{2} \times 14$
\[=539
\]
∴ Capacity of cylindrical cup is $\displaystyle 539 \mathrm{~cm}^{3}$
(iii)
External Curved surface area of cylindrical cup $\displaystyle =2 \times \frac{22}{7} \times \frac{7}{2} \times 14=308$
∴ External Curved surface area of cylindrical cup is $\displaystyle 308 \mathrm{~cm}^{2}$
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.