Question

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 information, answer the following questions.

1. Find the area of the base of the cylindrical cup.
2. What is the capacity of the hemispherical cup?
3. What is the capacity of the cylindrical cup?
4. Find the curved surface area of the cylindrical cup.

Answer 1

i. Area of the base of the cylindrical cup

Given: Diameter of the cylindrical cup, \[d = 7\text{ cm}\]

Radius of the base, \[r = \frac{7}{2}\text{ cm} = 3.5\text{ cm}\]

Formula: \[\text{Base Area} = \pi r^2\]

Calculation: \[\text{Base Area} = \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}\]

\[\text{Base Area} = \frac{77}{2} = 38.5\text{ cm}^2\]

ii. Capacity of the hemispherical cup

Given: Diameter of the hemispherical cup, \[D = 21\text{ cm}\]

Radius, \[R = \frac{21}{2}\text{ cm} = 10.5\text{ cm}\]

Formula: \[\text{Capacity} = \frac{2}{3}\pi R^3\]

Calculation: \[\text{Capacity} = \frac{2}{3} \times \frac{22}{7} \times \left(\frac{21}{2}\right)^3\]

\[\text{Capacity} = \frac{2}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}\]

\[\text{Capacity} = 11 \times \frac{441}{2} = 2425.5\text{ cm}^3\]

iii. Capacity of the cylindrical cup

Given: Radius of cylinder, \[r = \frac{7}{2}\text{ cm}\]

Height of cylinder, \[h = 14\text{ cm}\]

Formula: \[\text{Capacity} = \pi r^2 h\]

Calculation: \[\text{Capacity} = \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 14\]

\[\text{Capacity} = 77 \times 7 = 539\text{ cm}^3\]

iv. Curved surface area of the cylindrical cup

Formula: \[\text{CSA} = 2\pi rh\]

Calculation: \[\text{CSA} = 2 \times \frac{22}{7} \times \frac{7}{2} \times 14\]

\[\text{CSA} = 22 \times 14 = 308\text{ cm}^2\]