Mensuration Test

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Mensuration Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

The diameter of the base of a right circular cylinder is $$28$$ cm and its height is $$21$$ cm Curved surface area of the cylinder is

A
$$1540$$ $$\displaystyle cm^{2}$$

B
$$1648$$ $$\displaystyle cm^{2}$$

C
$$1848$$ $$\displaystyle cm^{2}$$

D
$$1548$$ $$\displaystyle cm^{2}$$

Solution

$$Diameter=28\ cm$$
$$\Rightarrow r=14\ cm$$
and $$ h =21 cm$$
C.S.A of cylinder$$\displaystyle =2\pi rh=2\times \dfrac{22}{7}\times 14\times 21=1848\ cm^{2}$$
Question 2
1 / -0

The volume of a right circular cylinder is 1100 $$\displaystyle cm^{3} $$ and the radius of its base is 5 cm. The area of its curved surface is

A
$$\displaystyle \left ( 440+25\pi \right )cm^{2} $$

B
$$\displaystyle \left ( 440+50\pi \right )cm^{2} $$

C
$$\displaystyle 440 cm^{2} $$

D
None of these

Solution

Volume of a cylinder$$=2\times\pi \times r\times h$$
$$\Rightarrow 1100=\displaystyle \dfrac{22}{7}\times 5^{2}\times h$$ {$$\because volume = 1100 \,cm^3\, is\, given$$}

$$\Rightarrow h =14cm$$

$$\therefore \displaystyle C.S.A =2\times \dfrac{22}{7}\times 5\times 14$$
$$\therefore C.S.A=440cm^{2}$$
Question 3
1 / -0

The diameter of a garden roller is $$1.4$$ m and it its $$2$$ m long. How much area will it cover in one revolution?

A
$$6.8$$ $$\displaystyle m^{2}$$

B
$$8.8$$ $$\displaystyle m^{2}$$

C
$$3.8$$ $$\displaystyle m^{2}$$

D
$$5.8$$ $$\displaystyle m^{2}$$

Solution

$$\Rightarrow$$ Diameter of the roller $$(d)=1.4\,m$$.

$$\Rightarrow$$ Radius of the roller $$(r)=\dfrac{1.4}{2}=0.7\,m.$$

$$\Rightarrow$$ Length of the roller $$(h)=2\,m.$$

If the roller complete one revolution

Then the area covered $$=$$ Curved surface area of the roller $$=2\pi r h$$

$$\Rightarrow$$ Area covered in $$1$$ revolution $$=2\pi r h$$

$$=2\times \dfrac{22}{7}\times 0.7\times 2\\$$
$$=88\times 0.1\\$$
$$=8.8\,m^2$$
Question 4
1 / -0

If the radius of the base of a cylinder is $$2$$ cm and its height $$7$$ cm, then what is its curved surface area?

A
$$44\:cm^2$$

B
$$22\:cm^2$$

C
$$88\:cm^2$$

D
$$56\:cm^2$$

Solution

Given, $$r=2$$ cm, $$h=7$$ cm

Then curved surface area $$=2 \pi r h$$

$$=2\times \dfrac{22}{7}\times 2\times 7$$

$$=88 cm^{2}$$
Question 5
1 / -0

The diameter of a garden roller is $$1.4\space m$$ and it is $$2\space m$$ long. How much area will it cover in $$5$$ revolutions? (Use $$\pi = \dfrac{22}{7}$$)

A
$$40\space m^2$$

B
$$41.40\space m^2$$

C
$$44\space m^2$$

D
$$42.40\space m^2$$

Solution

Since the diameter of the roller is
$$ 0.7 m $$, its radius is $$ 0.35 m $$.
The roller is in the shape of a cylinder.
In one revolution, the roller covers the distance of one curved surface area.
Curved Surface Area of a Cylinder of Radius "$$R$$" and height "$$h$$" $$= 2\pi Rh$$
Radius of the roller $$ = 0.7 m $$
Curved Surface Area of the roller of radius $$ 0.35 m = 2 \times \dfrac {22}{7}\times 0.7 \times 2 = 8.8 m^2 $$
Area covered in $$5$$ revolutions $$ = 5 \times 8.8 m^2 = 44 m^2 $$
Question 6
1 / -0

A metal pipe is $$77$$ cm long The inner diameter of a cross section is $$4$$ cm then inner curved surface area is

A
$$900$$ $$\displaystyle cm^{2}$$

B
$$960$$ $$\displaystyle cm^{2}$$

C
$$968$$ $$\displaystyle cm^{2}$$

D
$$964$$ $$\displaystyle cm^{2}$$

Solution

$$\Rightarrow$$ Diameter of inner section of pipe $$(d)=4\,cm$$

$$\Rightarrow$$ Radius of inner section of pipe $$(r)=\dfrac{4}{2}=2\,cm$$

$$\Rightarrow$$ Height of a pipe $$(h)=77\,cm$$

$$\Rightarrow$$ Inner surface area of a pipe $$=2\pi rh$$

$$=2\times \dfrac{22}{7}\times 2\times 77$$

$$=968\,cm^2$$
Question 7
1 / -0

Curved surface area of a right circular cylinder is $$4.4$$ $$\displaystyle m^{2}$$ If the radius of the base of the cylinder is $$0.7$$ m then its height is

A
$$2$$ m

B
$$3$$ m

C
$$4 $$m

D
$$1$$ m

Solution

Curved surface area $$=\displaystyle 2\pi rh=4.4$$

$$\Rightarrow 2\times \dfrac{22}{7}\times 0.7\times h=4.4\Rightarrow h=1m.$$
Question 8
1 / -0

Two tables with top faces as two congruent trapeziums are joined as shown. The lengths of the parallel sides are $$100\;cm\;and\;80\;cm$$ and the height is $$45\;cm$$. Find the combined table top area and the cost of polishing it at the rate of $$Rs.\;350$$ per $$m^2$$.

A
$$8110\;cm^2,\;Rs.\;238.5$$

B
$$8100\;cm^2,\;Rs.\;228.5$$

C
$$8100\;cm^2,\;Rs.\;233.5$$

D
$$8100\;cm^2,\;Rs.\;283.5$$

Solution

Combined area $$= 2$$ $$\times $$ area of $$1$$ table top
$$ =$$ $$2\times \dfrac { 1 }{ 2 } \times (\text{sum of parallel sides})\times h$$

$$=$$ $$\left( 100+80 \right) \times 45=8100{ cm }^{ 3 }=0.81{ m }^{ 2 }$$

Cost of polishing $$=$$ $$Rs.\left( 0.81\times 350 \right) =Rs.283.50$$
Question 9
1 / -0

Volume of the box of outer dimensions 22 cm X 12 cm X 9 cm

A
2276 $$\displaystyle cm^{3}$$

B
2500 $$\displaystyle cm^{3}$$

C
2600 $$\displaystyle cm^{3}$$

D
2376 $$\displaystyle cm^{3}$$

Solution

The dimensions of box are 24 cm ,22 cm and 17 cm
volume = $$l\times b\times h$$
volume =24 x 22 x 17 = 2376 cubic cm
Question 10
1 / -0

Total surface area of a cube of 2 centimetre side is

A
$$\displaystyle 20cm^{2}$$

B
$$\displaystyle 24cm^{2}$$

C
$$\displaystyle 25cm^{2}$$

D
$$\displaystyle 30cm^{2}$$

Solution

Total surface area of the cube=$$6a^2$$
Here a=2 cm
$$\Rightarrow 6\times (2^2)=24 cm^2$$

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Mensuration Test - 22

Result

Mensuration Test - 22

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Question 1

$$1540$$ $$\displaystyle cm^{2}$$

$$1648$$ $$\displaystyle cm^{2}$$

$$1848$$ $$\displaystyle cm^{2}$$

$$1548$$ $$\displaystyle cm^{2}$$

Solution

Question 2

$$\displaystyle \left ( 440+25\pi \right )cm^{2} $$

$$\displaystyle \left ( 440+50\pi \right )cm^{2} $$

$$\displaystyle 440 cm^{2} $$

None of these

Solution

Question 3

$$6.8$$ $$\displaystyle m^{2}$$

$$8.8$$ $$\displaystyle m^{2}$$

$$3.8$$ $$\displaystyle m^{2}$$

$$5.8$$ $$\displaystyle m^{2}$$

Solution

Question 4

$$44\:cm^2$$

$$22\:cm^2$$

$$88\:cm^2$$

$$56\:cm^2$$

Solution

Question 5

$$40\space m^2$$

$$41.40\space m^2$$

$$44\space m^2$$

$$42.40\space m^2$$

Solution

Question 6

$$900$$ $$\displaystyle cm^{2}$$

$$960$$ $$\displaystyle cm^{2}$$

$$968$$ $$\displaystyle cm^{2}$$

$$964$$ $$\displaystyle cm^{2}$$

Solution

Question 7

$$2$$ m

$$3$$ m

$$4 $$m

$$1$$ m

Solution

Question 8

$$8110\;cm^2,\;Rs.\;238.5$$

$$8100\;cm^2,\;Rs.\;228.5$$

$$8100\;cm^2,\;Rs.\;233.5$$

$$8100\;cm^2,\;Rs.\;283.5$$

Solution

Question 9

2276 $$\displaystyle cm^{3}$$

2500 $$\displaystyle cm^{3}$$

2600 $$\displaystyle cm^{3}$$

2376 $$\displaystyle cm^{3}$$

Solution

Question 10

$$\displaystyle 20cm^{2}$$

$$\displaystyle 24cm^{2}$$

$$\displaystyle 25cm^{2}$$

$$\displaystyle 30cm^{2}$$

Solution

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