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CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 12 - MCQExams.com
CBSE
Class 9 Maths
Surface Areas And Volumes
Quiz 12
A spherical iron ball $$10cm$$ in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$50cm^3/min$$, when the thickness of ice is $$5cm$$, then the rate at which the thickness of ice decreases is:
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$$\cfrac{1}{2\pi}cm/min$$
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$$\cfrac{1}{18\pi}cm/min$$
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$$\cfrac{1}{54\pi}cm/min$$
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$$\cfrac{5}{6\pi}cm/min$$
If the diameter of a sphere is 'd' then its volume is:
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$$\frac{1}{3} \pi d^3$$
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$$\frac{1}{2} \pi d^3$$
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$$\frac{4}{3} \pi d^3$$
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$$\frac{1}{6} \pi d^3$$
Explanation
We know that the volume of the sphere $$=\dfrac{4}{3}\pi r^3$$
Also, $$r = \dfrac{d}{2}$$
Therefore,
If the diameter of a sphere is 'd' then its volume = $$\dfrac{4}{3}\pi \left(\dfrac{d}{2}\right )^3 $$=
$$\dfrac{1}{6} \pi d^3$$
The diagram shows the net of a right cylinder. Find the volume of the cylinder, in cm$$^3$$
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$$\dfrac{20}{\pi}$$
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$$\dfrac{50}{\pi}$$
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$$\dfrac{25}{\pi}$$
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$$40 \pi$$
Find the ratio of the volume of sphere $$A$$ to sphere $$B$$, if the
ratio of the surface area of sphere $$A$$ to the surface area of sphere $$B$$ is $$729:1$$.
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$$27:1$$
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$$81:1$$
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$$19,683:1$$
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$$26,224:1$$
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$$531,441:1$$
Explanation
Let the radius of sphere $$A$$ be $$a$$ and the radius of sphere $$B$$ be $$b$$
Given, $$\dfrac {4 \pi {a}^{2} }{4\pi{b}^{2} }= 729$$
$$\Rightarrow \dfrac {{a}^{2}}{{b}^{2} }=\left(\dfrac{a}{b}\right)^2= 729=27^2$$
$$\Rightarrow \dfrac {a}{b} = 27$$
Ratio of volume of $$A$$ to volume of $$B$$ is $$\dfrac { \frac { 4 }{ 3 } \pi { a }^{ 3 } }{ \frac { 4 }{ 3 } \pi { b }^{ 3 } } $$
$$=\left (\dfrac {a}{b}\right)^3={ 27 }^{ 3 }$$
$$=19683$$
Sixteen cylindrical cans, each with a radius of 1 unit, are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and or the walls of the box, then which of the following could be the interior area of the bottom of the box is square units?
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16
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32
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64
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128
A spherical iron ball of volume $$720 \:cm^3$$ is immersed in a half-filled tank as shown in the figure.
Find the rise in the water level.
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3 cm
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$$3\frac{1}{2}\:cm$$
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$$4\frac{3}{4}\:cm$$
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6
cm
The curved surface of a hemisphere whose internal & external radii are $$a$$ and $$b$$ respectively, will be
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$$\displaystyle \pi \left( { a }^{ 2 }+{ b }^{ 2 } \right) $$
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$$\displaystyle 2\pi \left( { a }^{ 2 }+{ b }^{ 2 } \right) $$
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$$\displaystyle 2\pi \left( { a }^{ 2 }-{ b }^{ 2 } \right) $$
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$$\displaystyle 2\pi \left( { b }^{ 2 }+{ a }^{ 2 } \right) $$
Find the diameter of a sphere whose volume is $$113\cfrac{1}{7}$$ cubic metres.
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$$3m$$
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$$5m$$
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$$6m$$
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$$8m$$
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$$4m$$
How many litres of water (approximately) can a hemispherical container of radius $$21cm$$ hold?
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$$19.4$$
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$$38.8$$
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$$194$$
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$$388$$
$$12$$ litres of water are poured into an aquarium of dimensions $$50$$cm length, $$30$$cm breadth, and $$40$$cm height. How high (in cm) will the water rise?($$1$$ litre$$=1000cm^3$$)
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$$6$$
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$$8$$
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$$10$$
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$$20$$
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$$40$$
The weight of a sphere of iron of radius $$8cm$$ is $$1.2kg$$. What is the weight of a similar sphere whose radius is $$4cm$$?
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$$600$$ grams
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$$400$$ grams
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$$150$$ grams
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$$250$$ grams
When the radius of a sphere decreases from $$3\ cm$$ to $$2.98\ cm$$ then the approximately decrease in volume of sphere is
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$$0.002\pi \ \text{cm}^{3}$$
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$$0.072\pi \ \text{cm}^{3}$$
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$$0.72\pi \ \text{cm}^{3}$$
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$$0.008\pi \ \text{cm}^{3}$$
Explanation
Given radius of sphere decreases from 3 cm to 2.98 cm
volume of sphere $$ = \frac{4}{3}\pi r^{3}$$
$$ \triangle r = r_{2}-r_{1}$$
$$ = 2.98-3$$
$$ \triangle r = -0.02$$
$$ dr = -0.02 $$
consider $$ y = \frac{4}{3}\pi r^{3}$$
$$ \frac{dy}{dr} = \frac{4}{3}\pi 3r^{2}$$
$$ \frac{dy}{dr} = 4\pi r^{2}$$
$$ dy = 4\pi r^{2}.dr$$
$$ dy = 4\pi 3^{2}.(-0.02)$$
$$ dy = 4(3.14) 9(-0.02)$$
$$ dy = 36\pi (-0.02)$$
$$ dy = -0.72\pi \,cm^{3}$$
$$ \therefore $$ The volume of sphere
decrease by $$ -0.72 \pi \,cm^{3}$$
Three solid metallic spheres of radii $$6$$, $$8$$ and $$10$$ centimetres are melted to form a single solid sphere. The radius of the sphere so formed is __________.
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$$24$$cm
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$$16$$cm
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$$18$$cm
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$$12$$cm
Explanation
Given are three metallic spheres of radius $$6,8,10$$ cm.
They are melted to form a single solid sphere.
Now,
Volume of the single solid sphere=Volume of the three spheres
Say the radius of the resulting sphere is $$r$$ cm.
$$\therefore \cfrac { 4 }{ 3 } \pi { r }^{ 3 }=\cfrac { 4 }{ 3 } \pi { (6) }^{ 3 }+\cfrac { 4 }{ 3 } \pi { (8) }^{ 3 }+\cfrac { 4 }{ 3 } \pi { (10) }^{ 3 }\\ =>{ r }^{ 3 }={ 6 }^{ 3 }+{ 8 }^{ 3 }+{ 10 }^{ 3 }$$
$$=>r={ \left( 1728 \right) }^{ \cfrac { 1 }{ 3 } }=12$$cm
The largest sphere is cut off from a cube of side 5cm. The volume of the sphere will be_
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$$
27 \pi \mathrm{cm}^{3}
$$
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$$
30 \pi \mathrm{cm}^{3}
$$
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$$
108 \pi \mathrm{cm}^{3}
$$
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$$
\frac{125}{6} \pi \mathrm{cm}^{3}
$$
The volume of a sphere is $$36\prod c{m^2} $$. Then is diameter is ___ cm.
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6
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12
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3
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9
If the surface area of a sphere is $$144\pi\ m^2$$, then its volume is
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$$288 \pi\ m^3$$
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$$316 \pi\ m^3$$
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$$300 \pi\ m^3$$
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$$188 \pi\ m^3$$
Explanation
Let the radius of the sphere be $$r.$$
Surface area of a sphere $$ = 144\pi$$
$$4\pi r^2=144\pi$$
$$r^2=36$$
$$r = 6\ m$$
Now,
Volume of a sphere $$=\dfrac43 \pi r^3$$
$$=\dfrac43\pi \times 6^3$$
$$=288\pi\ m^3$$
Hence, option $$A$$ is correct.
Area of Sphere varies with the square of radius. Given that the area of sphere is $$216sq$$ units, when the radius is $$6$$ units, find the area of sphere when the radius is $$5$$ units.
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$$180sq$$ units
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$$240sq$$units
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$$210sq$$ units
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$$150sq$$ units
A water tank has a capacity of $$10,000$$ litre. Its value in $$m ^ { 3 }$$ is
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10$$\mathrm { m } ^ { 3 }$$
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1000$$\mathrm { m } ^ { 3 }$$
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1$$\mathrm { m } ^ { 3 }$$
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none
A right circular cylinder just encloses a sphere of radius $$r$$. Find the ratio of the s
urface areas of the sphere and the cylinder.
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$$\dfrac{2}{3}$$
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$$\dfrac{1}{3}$$
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$$\dfrac{3}{2}$$
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$$\dfrac{4}{5}$$
A dome of a building is in the form of a hemisphere from inside, it was whitewashed at the cost of Rs $$498.96$$
. If the cost of white-washing is
498.96
RS $$2.00$$ per square meter, find
Inside surface area of the dome
Volume of the air inside the dome
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$$249.98~ \text{m}^2$$ and $$523.9~\text{m}^3$$
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$$248.8~ \text{m}^2$$ and $$523.9~\text{m}^3$$
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$$249~ \text{m}^2$$ and $$523.9~\text{m}^3$$
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$$249.48~ \text{m}^2$$ and $$523.9~\text{m}^3$$
How many lead balls each of radius 4 cm can be made by melting a lead sphered of diameter 40 cm?
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1000
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500
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250
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125
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