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In a coffee shop, coffee is served in two types of cups. One is cylindrical shape with each of diameter $8$ cm and height $7$ cm and the other hemispherical with each of diameter $14$ cm.
Based on the above, answer the following questions :
(i) What is the outer curved surface area of the cylindrical cup ?
(ii) What is the inner surface area of the hemispherical cup ?
(iii) (a) Find the difference of the capacities of the two cups.
OR
(b) Find the total volume of coffee in two cylindrical and one hemispherical cup.
Based on the above, answer the following questions :
(i) What is the outer curved surface area of the cylindrical cup ?
(ii) What is the inner surface area of the hemispherical cup ?
(iii) (a) Find the difference of the capacities of the two cups.
OR
(b) Find the total volume of coffee in two cylindrical and one hemispherical cup.
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Solution:
(i) $r = 4$ cm
Outer C.S.A. of cylindrical cup = $2 \times \frac{22}{7} \times 4 \times 7 = 176$ cm$^2$ (1 Mark)
(ii) $R = 7$ cm,
Inner Surface Area of hemispherical cup = $2 \times \frac{22}{7} \times 7 \times 7 = 308$ cm$^2$ (1 Mark)
(iii) (a) Difference in the capacities = $\frac{22}{7} \times 4 \times 4 \times 7 - \frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$ (1 Mark)
$= \frac{1100}{3}$ cm$^3$ or $366.67$ cm$^3$ (1 Mark)
OR
(b) Total Volume of coffee = $2 \times \frac{22}{7} \times 4 \times 4 \times 7 + \frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$ (1 Mark)
$= \frac{4268}{3}$ cm$^3$ or $1422.67$ cm$^3$ (1 Mark)
(i) $r = 4$ cm
Outer C.S.A. of cylindrical cup = $2 \times \frac{22}{7} \times 4 \times 7 = 176$ cm$^2$ (1 Mark)
(ii) $R = 7$ cm,
Inner Surface Area of hemispherical cup = $2 \times \frac{22}{7} \times 7 \times 7 = 308$ cm$^2$ (1 Mark)
(iii) (a) Difference in the capacities = $\frac{22}{7} \times 4 \times 4 \times 7 - \frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$ (1 Mark)
$= \frac{1100}{3}$ cm$^3$ or $366.67$ cm$^3$ (1 Mark)
OR
(b) Total Volume of coffee = $2 \times \frac{22}{7} \times 4 \times 4 \times 7 + \frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$ (1 Mark)
$= \frac{4268}{3}$ cm$^3$ or $1422.67$ cm$^3$ (1 Mark)