Math, asked by canitiya02, 6 months ago

find the cylinder glass of diameter 6cm and h=80mm that can be filled with juice from cylinder vessel of diameter 30 CM given that the vessel is filled with juice h=32 cm​

Answers

Answered by aryan073
4

Given :

• Height of vessel (H) =32cm

• Diameter of vessel(D)=30cm

\sf{\dfrac{30}{2}=15cm}

ie, Radius of vessel=15cm

• Height of Glass(h)=80mm=8cm

•Diameter of Glass(d)=6cm

\sf{\dfrac{6}{2}=3cm}

________________________________________

Solution :

➡ Let the number of glasses that can be filled ='x'

According to given conditions :

Therefore,

The volume of vessel=x times of the volume of the glass

\\ \implies\sf{\pi R^{2} H=\pi r^{2} h \times x}

\\ \implies\sf{\pi(15)^2 \times 32 = \pi (3)^2 \times 8 \times x}

  \\ \implies \sf \: \pi {(15)}^{2}  \times 32 = \pi {(3)}^{2}  \times 8 \times x \\  \\    \\  \implies \sf \:   \cancel{\pi }225 \times 32 =  \cancel{\pi} \times 9 \times 8 \times x \\  \\  \\  \implies \sf225 \times 32 = 9 \times 8 \times x \\  \\   \\ \implies \sf \:  \frac{225 \times 32}{9 \times 8}  = x \\  \\  \\  \implies \sf \: x =  \frac{ \cancel{ {225}}^{25}  \times  \cancel{ {32}}^{4} }{ \cancel9 \times  \cancel8}  \\  \\  \\  \implies \sf \: x = 25 \times 4 = 100 \\  \\  \\  \implies \boxed { \sf{x = 100}}

➡ Therefore, the number of glasses that can be filled =x=100

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