Question

CBSE CLASS X

MATHEMATICS

SURFACE AREA AND VOLUMES

Shyam and his wife radha are making Jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone, the diameters of whose circular ends are 30 cm and 35 cm and whose height is 14 cm. If the mass of 1 cubic cm of molasses is 1.2 g, find the mass of the molasses that can be poured in each mould.

$Use\: \pi = \frac{22}{7}$

Answer 1

volume of frustum= pie/3 h (R^2 + r^2 + R×r)

As diameter = 30 and 35

R= 35/2

r= 30/2= 15

So volume = 22/7× 3 ) × 14 ( 17.5)^2 + 15^2 + 17.5×15)

= 132 ( 306.25 + 225 +262.5)

= 132( 793.75)

= 104775 cm^3

As mass of 1cm^3 is 1.2g

So mass of 104775 cm^3 is 104775× 1.2 = 125730 g= 125.73kg

Answer 2

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${\boxed {\boxed{ \sf{Here's \: the \: answer}}}}$


Answer : 14 kg ( approx )

(Refer the attachment) :)

Step-by-step explanation :


Here,
We have to find mass of molasses.

In simple words,

We have to find it's volume.

As the moulds are in shape of frustum,

Volume of molasses = Volume of frustum

$\sf{= \frac{1}{3} \times \pi \: h( r_{1} {}^{2} + r_{2} {}^{2} + r_1{ r_{2} })}$

So,
Diameter of the large circular face = 35

$\therefore\sf{r_{1} = \frac{35}{2} }$

Diameter of the small circular face = 30

$\sf{ \therefore \sf \: r_{2} = \frac{30}{2} = 15}$

Height = 14 cm

As per the volume formula for frustum ,

$\sf \tiny{ = \frac{1}{3} \times \frac{22}{7} \times 14 \times ((15) {}^{2} + {(\frac{35}{2})} ^{2} + 15 \times \frac{35}{2})}$

$\small \sf{= \frac{44}{3} \times 225 + \frac{1225}{4} + \frac{525}{2} }$

$\sf{ = \frac{44}{3} \times \frac{(225 \times 4 + 1225 \times 525 \times 2)}{4}}$

$\sf {= \frac{44}{3} \times \frac{(900 \: + \: 1225 + \: 1050)}{4} }$

$\sf{= \frac{44}{3} \times \frac{3175}{4}}$

$\sf{ = \frac{11}{3} \times 3175}$

$\sf {= \frac{34925}{3}}$

$\sf{= 11641.66 \: cm {}^{3} }$

Now,

1.3 cm^3 molasses has mass 1.2 grams

So,
11641.66 cm^3 molasses has mass

= 11641.66 × 1.2

= 13970 grams

Converting into kg,

$\sf{= 13970 \times \frac{1}{1000}}$

$\sf {= 13.97 \: kg}$

$\sf {\approx 14 \: kg}$

Therefore,

Mass of the molasses is approximately 14 kg.

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