Question

24. A juiceseller has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in cylindrical glasses of radius 3 cm up to a height of 8 cm, and sold for ₹15 each. How much money does he receive by selling the juice completely?​

Answer 1

$\large\underline{\sf{Solution-}}$

Dimensions of cylindrical vessel

Radius, r = 15 cm

Height, h = 32 cm

So,

$\rm \: Volume_{(Cylindrical\:vessel)} = \pi \: {r}^{2}h$

$\rm \: Volume_{(Cylindrical\:vessel)} = \pi \: {(15)}^{2} \times 32 \: {cm}^{3}$

Dimensions of cylindrical glass

Radius, R = 3 cm

Height, H = 8 cm

So,

$\rm \: Volume_{(Cylindrical\:glass)} = \pi {R }^{2}H$

$\rm \: Volume_{(Cylindrical\:glass)} = \pi {(3) }^{2} \times 8 \: {cm}^{3}$

Let assume that number of cylindrical glasses be n.

So,

$\rm \: n \times Volume_{(Cylindrical\:glass)} = Volume_{(Cylindrical\:vessel)}$

$\rm \: n \times \pi {(3)}^{2} \times 8 = \pi {(15)}^{2} \times 32$

$\rm \: n \times 3 \times 3 = 15 \times 15 \times 8$

$\rm \: n = 5 \times 5 \times 8$

$\rm\implies \:n \: = \: 200$

Now, Selling Price of 1 cylindrical glass = ₹ 15

So, Selling Price of 200 cylindrical glass = 15 × 200 = ₹ 3000

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$