52
Case Study - 2
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 hemispherical with diameter $21$ 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
(ii) (b) 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 $7$ cm and height $14$ cm and the other is hemispherical with diameter $21$ 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
(ii) (b) Find the capacity of the cylindrical cup.
(iii) What is the curved surface area of the cylindrical cup?
Show SolutionHide Solution↓
(i) Area of base of the cylindrical cup = $\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} = \frac{77}{2}$ or $38.5$
$\therefore$ Area of base of the cylindrical cup is $\frac{77}{2}$ or $38.5$ cm$^2$
(ii) (a) Capacity of hemispherical cup = $\frac{2}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}$
$= \frac{4851}{2}$ or $2425.5$
$\therefore$ Capacity of hemispherical cup is $\frac{4851}{2}$ cm$^3$ or $2425.5$ cm$^3$
OR
(ii) (b) Capacity of cylindrical cup = $\frac{22}{7} \times (7)^2 \times 14$
$= 539$
$\therefore$ Capacity of cylindrical cup is $539$ cm$^3$
(iii) External Curved surface area of cylindrical cup = $2 \times \frac{22}{7} \times \frac{7}{2} \times 14 = 308$
$\therefore$ External Curved surface area of cylindrical cup is $308$ cm$^2$
$\therefore$ Area of base of the cylindrical cup is $\frac{77}{2}$ or $38.5$ cm$^2$
(ii) (a) Capacity of hemispherical cup = $\frac{2}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}$
$= \frac{4851}{2}$ or $2425.5$
$\therefore$ Capacity of hemispherical cup is $\frac{4851}{2}$ cm$^3$ or $2425.5$ cm$^3$
OR
(ii) (b) Capacity of cylindrical cup = $\frac{22}{7} \times (7)^2 \times 14$
$= 539$
$\therefore$ Capacity of cylindrical cup is $539$ cm$^3$
(iii) External Curved surface area of cylindrical cup = $2 \times \frac{22}{7} \times \frac{7}{2} \times 14 = 308$
$\therefore$ External Curved surface area of cylindrical cup is $308$ cm$^2$