A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. [3 MARKS]

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Solution

Formula: 1 Mark
Application: 1 Mark
Answer: 1 Mark

Volume of hemisphere = Volume of cone
$\Rightarrow \frac{2}{3} π r^{3} = \frac{1}{3} π r^{2} h$
$\Rightarrow \frac{2}{3} \times 3.6 \times 3.6 \times 3.6 = \frac{1}{3} \times 4.8 \times 4.8 \times h$
$\Rightarrow h = \frac{3.6 \times 3.6 \times 3.6 \times 2}{4.8 \times 4.8} = 4.05 c m$
Hence, the height of the cone is 4.05 cm

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A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. [3 MARKS]

Formula: 1 Mark Application: 1 Mark Answer: 1 Mark Volume of hemisphere = Volume of cone ⇒23πr3=13πr2h ⇒23×3.6×3.6×3.6=13×4.8×4.8×h ⇒h=3.6×3.6×3.6×24.8×4.8=4.05 cm Hence, the height of the cone is 4.05 cm