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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 $\displaystyle 7$ 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)What is the capacity of the hemispherical cup ?Find the capacity of the cylindrical cup.(iii)What is the curved surface area of the cylindrical cup ?
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)
What is the capacity of the hemispherical cup ?
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)
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 $\displaystyle 2425.5 \mathrm{~cm}^{3}$
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 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.