In a coffee shop, coffee is served in two types of cups. One type i...

Question

In a coffee shop, coffee is served in two types of cups. One type is cylindrical with each of diameter 8 cm and height 7 cm, while the other type is hemispherical with each of diameter 14 cm.
(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
(iii)(b) Find the total volume of coffee in two cylindrical and one hemispherical cup.

Accepted Answer

Cylindrical cup: radius $r=4$ cm, height $h=7$ cm. Hemispherical cup: radius $R=7$ cm.

(i) $$CSA(	ext{cylinder})=2\pi rh=2	imes\frac{22}{7}	imes4	imes7=176\ cm^2$$

(ii) $$	ext{Inner surface area (hemisphere)}=2\pi R^2=2	imes\frac{22}{7}	imes49=308\ cm^2$$

(iii)(a) $$V(	ext{cylinder})=\pi r^2h=\frac{22}{7}	imes16	imes7=352\ cm^3$$ $$V(	ext{hemisphere})=\frac23\pi R^3=\frac23	imes\frac{22}{7}	imes343=\frac{2156}{3}\approx718.67\ cm^3$$ Difference $=718.67-352\approx366.67\ cm^3\left(=\frac{1100}{3}\ cm^3ight)$

OR

(iii)(b) Total volume $=2(352)+718.67=704+718.67\approx1422.67\ cm^3\left(=\frac{4268}{3}\ cm^3ight)$

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