Question

A container in the shape of of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely filled with oil. if each of oil has mass 1.2 g, then find the cost of oil in the container if it costs ₹40 per kg.​

Answer 1

Answer:

Diameter of top of container = 35 cm

Radius of top = R = 35/2 = 17.5 cm

Diameter of bottom of container = 30 cm

Radius of bottom = r = 30/2 = 15 cm 1 cm3 of oil = 1.2g of oil, so

Cost of 1 kg oil = Rs. 40

Height of frustum = h = 14 cm

Volume of frustum of cone = 1/3π h(R2 + r2 + Rr) cm3

Volume of oil in container = 1/3 x 22/7 x 14(17.52 + 152 + 17.5 x 15) = 22/3 × 2 × 793.75 =34925/3

Volume of oil in container = 11641.667 cm3 or 11641.667 × 1.2 g = 13970.0004 g or 13.970 kg (As 1000 g = 1 kg)

Cost of 13.970 kg oil = Rs. 20 x 13.970 = Rs. 558.8

Answer 2

QuestioN:

• A container in the shape of of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely filled with oil. if each of oil has mass 1.2 g, then find the cost of oil in the container if it costs ₹40 per kg.

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${\large{\frak{\pmb{\underline{ Clearly,\:we\: have}}}}}$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ\:r = \bf\dfrac{30}{2}\:cm=15\:cm$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ\:R = \bf\dfrac{35}{2}\:cm=17.5\:cm$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\succ\:h = 14\:cm$

$\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━━$

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${\bold { \underline{\small{Now,}}}}$

$\:\:\Large{\ddagger}\underline {\footnotesize{\boxed{\frak{Volume_{(container)}={\frak{\purple{\bigg\{\bf\dfrac{1}{3}\pi (R^2+r^2+Rr)h\bigg\}cu}}}}}}}$

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$\:$

$\sf {\scriptsize\Bigg[\bf\dfrac{1}{3}\times \bf\dfrac{22}{7}\times\Bigg\{\bigg(\dfrac{35}{2}\bigg)^2+(15)^2+\dfrac{35}{2}\times 15\Bigg\}\times 14 \Bigg]cm^3}$

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$\sf \:\:\:\:\:\rightarrowtail\: \dfrac{44}{3}\times\bigg(\dfrac{1225}{4}+225+\dfrac{525}{2}\bigg)cm^3$

$\:\:$

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$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\rightarrowtail\: \bigg( \dfrac{44}{3}\times \dfrac{3175}{4}\bigg)cm^3$

$\:\:$

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$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\rightarrowtail\: \bigg( \dfrac{3175 \times 11}{3}\bigg)cm^3$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\small{\underline{\mathcal{\pink{Mass\:of\:1\:cm^3\:of\:oil\:=\:1.2\:g }}}}$

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$\:\:\:\:\:\:\:\sf \footnotesize{Mass_{(oil\:in\:the\: container)}=\bigg( \dfrac{3175 \times 11}{3}\times1.2 \bigg)\:g}$

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$\sf\:\:\:\:\:\:\:\:\rightarrowtail\:\bigg( \dfrac{3175 \times 11}{3}\times\dfrac{12}{10}\times\dfrac{1}{1000}\bigg)\:kg$

$\:\:$

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$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\rightarrowtail\:\dfrac{1397}{100}\:kg\:=13.97\:kg$

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• $\bf\twoheadrightarrow$Cost of oil at ₹40 per kg = ₹(13.97×40)$\:\:=\:\large{\underline{\mathcal{\orange{ ₹\:558.80.}}}}$