Question

A drinking glass is in the shape of a frustum of a cone of height 14cm. The diameters of its two circular ends are 4cm and 2cm. Find the capacity of the glass.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Volume\:of\:glass=102.67\:cm^{3}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: {\implies Height \: of \: glass = 14 \: cm} \\ \\ \tt: {\implies Diameter \: of \: glass ( d_{1})=4 \: cm} \\ \\ \tt: {\implies Diameter \: of \: glass ( d_{2})=2\: cm} \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Volume \: of \: glass = ?$

• According to given question :

$\tt \circ \: r_{1} = 2 \: cm \\ \\ \tt \circ \: r_{2} = 1 \: cm \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: glass = \frac{1}{3} \pi h(( r_{1})^{2} + {( r_{2} )}^{2} + ( r_{1} \times r_{2})) \\ \\ \tt: \implies Volume \: of \: glass = \frac{1}{3} \times \frac{22}{7} \times 14 \times ( {2}^{2} + {1}^{2} + (2 \times 1)) \\ \\ \tt: \implies Volume \: of \: glass = \frac{1}{3} \times 44 \times (4 + 1 + 2) \\ \\ \tt: \implies Volume \: of \: glass = \frac{1}{3} \times 44 \times 7 \\ \\ \green{\tt: \implies Volume \: of \: glass = 102.67 \: {cm}^{3} }$

Answer 2

ANSWER

102.58 cm^2

FORMULA USED

VOLUME OF FRUSTOM = π/3 ×h(R^2+r^2+R×r)

EXPLANATION

Given

diameter = 4cm and 2 cm and height 14 cm

radius = 2 cm and 1 cm

CAPACITY = VOLUME OF FRUSTEM

= π/3 × (14)(4+1+2)

= 102.58 cm^2

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