Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

The capacity of a water tank that measures $$9$$ cm $$\times 3.5$$ cm $$\times 7.5$$ cm is

A
$$236.25$$ c$$m^3$$

B
$$189$$ $$cm^3$$

C
$$236.25$$ $$m^3$$

D
$$189$$ $$m^3$$

Solution

Here, length $$= 9$$ cm, breadth $$= 3.5$$ cm and height $$= 7.5$$ cm
$$\therefore $$ capacity of water tank $$= $$ length $$\times$$ breadth $$\times$$ height
$$=9 \times 3.5 \times 7.5 = 236.25$$ $$cm^3$$ .
Question 2
1 / -0

A godown measures 40 m $$\times$$ 25 m $$\times$$ 10 m The maximum number of wooden crates each measuring 1.0 m $$\times$$ 1.25 m $$\times$$ 0.5 m that can be stored in the godown is:

A
14000

B
18000

C
15000

D
16000

Solution

Both godown and wooden crates are of the shape of a cuboid.

Volume of a cuboid of length l, breadth b and height h $$ = l

\times b \times h $$.

Number of wooden crates that can be stored $$ = \dfrac {Volume \quad of \quad the \quad go-down}{Volume \quad of \quad one \quad wooden \quad crate} = \dfrac {40

\times 25 \times 10}{1 \times 1.25 \times 0.5} = 16000 $$
Question 3
1 / -0

How many bricks, each measuring $$25 cm \times 11.25 cm \times 6 cm$$ will be needed to build a wall $$8 m \times 6 m \times 22.5 cm$$ ?

A
$$5600$$

B
$$6000$$

C
$$6400$$

D
$$7200$$

Solution

Number of bricks $$=\, \displaystyle \frac{Volume\, of\, wall}{Volume\, of\, 1\, brick}$$

$$=\, \displaystyle \frac{800\, \times\, 600\, \times\, 22.5}{25\, \times\, 11.25\, \times\, 6}$$ ....$$(1m = 100 cm)$$

$$= 6400.$$
Question 4
1 / -0

The volume of air in a room $$10 m$$ long, $$6.5 m$$ wide, and $$5 m$$ height is:

A
$$425$$ cu m

B
$$225$$ cu m

C
$$325$$ cu m

D
None of the above

Solution

$$l=10m,b=6.5m,h=5m$$
Volume of air$$=l\times b\times h=10\times 6.5\times 5=325m^3$$
Question 5
1 / -0

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape It is $$30\ cm$$ long, $$25\ cm$$ wide, and $$25\ cm$$ high The area of glass is:

A
$$5000\ cm^{2}$$

B
$$ 4800\ cm^{2}$$

C
$$4250\ cm^{2}$$

D
$$4500\ cm^{2}$$

Solution

Since the greenhouse is cuboidal in shape, we need to calculate its total surface area by applying the formula.
Total surface area of a cuboid $$ = 2(l \times b + b\times h + l \times h) $$
Given:-
$$l=30\ cm$$
$$b=25\ cm$$
$$h=25\ cm$$

Hence, the total surface area of the herbarium will be,
$$S =2(30 \times 25 + 25 \times 25 + 30 \times 25) $$
$$= 2(750+625+750) $$
$$=2(2125)$$
$$= 4250 \ cm^2$$
Question 6
1 / -0

Find the volume of a cuboid of length $$20$$ cm, breadth $$15$$ cm and height $$10$$ cm.

A
$$8794$$ $$cm^3$$

B
$$7680$$ $$cm^3$$

C
$$3000$$ $$cm^3$$

D
$$5760$$ $$cm^3$$

Solution

Given, length of the cuboid$$ = 20$$ cm
Breadth of the cuboid $$= 15$$ cm
Height of the cuboid$$ = 10$$ cm
$$\therefore$$ Volume of the cuboid $$=$$ length $$\times$$ breadth $$\times$$ height
$$=3000 cm^3$$
Question 7
1 / -0

A cuboid is $$3$$ cm high, $$4$$cm wide and $$5$$cm long. What is its volume?

A
$$60 cm^3$$

B
$$50 cm^3$$

C
$$150 cm^3$$

D
$$100 cm^3$$

Solution

$$Volume\ of\ cuboid=length*breadth*height$$
$$length=5\ cm$$
$$breadth=4\ cm$$
$$height=3\ cm$$
$$Volume=5*4*3=60\ cm^3$$
Question 8
1 / -0

A plastic box $$1.5$$ m long, $$1.25$$ m wide, and $$65$$ cm deep is to be made. It is to be opened at the top. Ignoring the thickness of the plastic, the cost of the sheet for covering it, if a sheet measuring $$1$$$$\displaystyle m^{2}$$ costs Rs. $$20$$ is:

A
Rs. $$100$$

B
Rs. $$109$$

C
Rs. $$115$$

D
Rs. $$110$$

Solution

Length of the box, $$l=1.5m$$. Breadth of box,$$b=1.25m$$

Depth of box, $$h=65cm=0.65m$$

Area of sheet required$$=$$ Area of cuboid$$-$$Area of open top

$$=2(lb+bh+hl)-lb$$

$$=lb+2h(b+l)$$

$$=1.5\times 1.25+2\times 0.65(1.5+1.25)$$

$$=5.45m^2$$

Cost of sheet of $$5.45m^2=$$Rs. $$(5.45\times 20)=$$Rs. $$109$$
Question 9
1 / -0

The radius of the cylinder whose lateral surface area is $$704\, cm^2$$ and height $$8$$ cm is

A
$$6$$ cm

B
$$4$$ cm

C
$$8$$ cm

D
$$14$$ cm

Solution

Lateral surface area of a cylinder $$=2 \pi r h$$
Given, $$\, 2\, \pi\, rh\, =\, 704\, cm^2$$.
$$\therefore\, r\, =\, \displaystyle \frac {704}{2\pi h}\, $$
$$=\, \displaystyle \frac {704}{2\, \times\, \displaystyle \frac {22}{7}\, \times\, \times\, 8}\, $$
$$=\, 14$$ cm
Question 10
1 / -0

If a cistern is $$3$$ metres long, $$2$$ metres wide and $$1$$ metre deep, its capacity is

A
$$6000$$ litres

B
$$600$$ litres

C
$$60$$ litres

D
$$6$$ litres

Solution

Capacity of cistern $$=\, l\, \times\, b\, \times\, h$$
$$=\, 3\, m\, \times\, 2\, m\, \times\, 1\, m\, =\, 6\, m^3=\, 6000\, litres$$.

$$(\therefore\, 1\, m^3\, =\, 1000\, L)$$

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Surface Areas and Volumes Test - 28

Result

Surface Areas and Volumes Test - 28

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SHARING IS CARING

Question 1

$$236.25$$ c$$m^3$$

$$189$$ $$cm^3$$

$$236.25$$ $$m^3$$

$$189$$ $$m^3$$

Solution

Question 2

14000

18000

15000

16000

Solution

Question 3

$$5600$$

$$6000$$

$$6400$$

$$7200$$

Solution

Question 4

$$425$$ cu m

$$225$$ cu m

$$325$$ cu m

None of the above

Solution

Question 5

$$5000\ cm^{2}$$

$$ 4800\ cm^{2}$$

$$4250\ cm^{2}$$

$$4500\ cm^{2}$$

Solution

Question 6

$$8794$$ $$cm^3$$

$$7680$$ $$cm^3$$

$$3000$$ $$cm^3$$

$$5760$$ $$cm^3$$

Solution

Question 7

$$60 cm^3$$

$$50 cm^3$$

$$150 cm^3$$

$$100 cm^3$$

Solution

Question 8

Rs. $$100$$

Rs. $$109$$

Rs. $$115$$

Rs. $$110$$

Solution

Question 9

$$6$$ cm

$$4$$ cm

$$8$$ cm

$$14$$ cm

Solution

Question 10

$$6000$$ litres

$$600$$ litres

$$60$$ litres

$$6$$ litres

Solution

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