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Given a cuboid tank, in which situation will you find surface area and in which situation volume.

(a) To find how much it can hold.

(b) Number of paint bottle required to paint it.

(c) To find the number of smaller tanks that can be filled with water from it.

(a) Volume

(b) Surface Area

(c) Volume

Compare the volumes

(a) Cube (side =12 cm)

Cuboid (L=11 cm, B=12 cm, H=13 cm)

(b) Cylinder ( r=10 cm , H=14 cm)

Cuboid (L=10 cm, B=11 cm, H=14 cm)

(a) Volume of Cube =12^{3} =1728

Volume of Cuboid =11 *12 * 13 =1716

So cube is having more volume

(b) Volume of cylinder= π (10)^{2} 14 =4400

Volume of Cuboid =10 *11 * 14 =1540

So cylinder is having more volume

Find following

(a) the height of a cuboid whose base area is 180 cm

(b) The side of cube whose volume is 64 m

(c) Volume of the cylinder whose base area is 20 cm

(a) Volume = $L \times B \times H = (L \times B) \times H =\text(Base Area) \times H$

$900=180 \times H$
or H=5 cm

(b) Volume of Cube = (side)^{3}

$\text{side} =\sqrt [3] {Volume} = 4 \ cm$

(c) Volume of Cylinder = $ \pi r^2 h = (\pi r^2) \times h = \text{base area} \times h = 20 \times 10 =200 \ cm^2$

A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 12 cm can be placed in the given cuboid?

Volume of Cuboid= 60 × 54 × 30 =97200 cm^{3}

Volume of Cube = (12)^{3}=1728 cm^{3}

Total number of cube which can be placed in cuboid= 97200/1728= 56.25 =56

Find the height of the cylinder whose volume is 2.54 m³ and diameter of the base is 140 cm?

Volume of Cylinder = $ \pi r^2 h= \frac {\pi D^2 h}{4}$

Therefore

$\frac {\pi (1.4)^2 h}{4}= 2.54$

h=1.64 m

A water tank is in the form of cuboid whose length is 1.5 m , height is 2 m and Breath is 7 m. Find the quantity of water in litres that can be stored in the tank?

Volume of water tank=1.5 × 2 × 7 =21 m^{3}

Now 1m^{3}=1000 L

So quantity of water stored= 21000 L

If each edge of a cube is quadrupled,

(i) how many times will its surface area increase?

(ii) how many times will its volume increase?

$V_1=L^3$ and $SA_1= 6L^2$

$V_2= (4L)^3 = 64L^3$ and $SA_2=6(4L)^2 = 16 \times 6L^2$

So, Volume becomes 64 times and Surface Area become 16 times

Water is pouring into a cuboidal reservoir at the rate of 60 liters per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.

volume of reservoir = 108 m³=108000 L

Number of minute= 108000 /60=1800 minutes= 30 hours

If Length, Breath, Height of a cuboid is tripled,

(i) how many times will its surface area increase?

(ii) how many times will its volume increase?

$V=LBH$ and $SA= 2(LB + BH+ LH)$

If Length, Breath, Height of a cuboid is tripled

$V_f= 3L \times 3B \times 3H= 27 LBH$

$SA_F= 2(3L \times 3B + 3B \times 3H + 3L \times 3H)=9 \times 2(LB + BH+ LH) $

So volumen increased by 27 times and Surface area increased by 9 times

If radius of cylinder is tripled and height remains same

(i) how many times will its lateral surface area increase?

(ii) how many times will its volume increase?

$V= \pi r^2 h$ and $SA= 2 \pi rh$

If radius of cylinder is tripled and height remains same,then

$V_2= \pi (3r)^2 h = 9 \pi r^2 h$

$SA_2 = 2 \pi (3r) h =3 \times 2 \pi rh$

So volume becomes 9 times and Surface area becomes 3 times

This Extra questions for Mensurations Class 8 Maths is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.

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