Surface Areas and Volumes Test

Result

Surface Areas and Volumes Test - 50

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?

A
$$1:8$$

B
$$1:4$$

C
$$1:27$$

D
$$8:1$$

Solution

Let $$ V_1 $$ and $$ V_2 $$ be the volumes of first and second sphere respectively. Then,

$$ \dfrac{V_1}{V_2} = \dfrac{\left ( \dfrac 4 3 \right )\pi r^3}{\left (\dfrac 4 3 \right )\pi \left ( 2r \right )^{3}} = \dfrac{1}{8}$$
Question 2
1 / -0

The surface area of a $$10\ cm \times 4\ cm\times 6\ cm$$ brick is

A
$$84\ cm^2$$

B
$$124\ cm^2$$

C
$$164\ cm^2$$

D
$$180\ cm^2$$

Solution

We know that the total surface area of cuboid $$=2(lb+bh+hl)$$

So, the surface area of the brick $$=2(10\times 6+4\times 6+ 4\times 10)$$

$$=2(40+30+12)$$

$$=164$$
Question 3
1 / -0

The area of the cardboard needed to make a box of size $$25\ cm\times 15\ cm\times 8\ cm$$ will be

A
$$390\ cm^2$$

B
$$1390\ cm^2$$

C
$$2780\ cm^2$$

D
$$1000\ cm^2$$

Solution

We know that total surface area of cuboid $$=2(lb+bh+hl)$$
$$=2(25\times15+15\times8+8\times25)$$
$$=2(375+120+200)$$
$$=1390\ cm^2$$
Question 4
1 / -0

Volume of two spheres are in the ratio $$64 : 27$$. The ratio of their surface areas is:

A
$$3:4$$

B
$$4:3$$

C
$$9:16$$

D
$$16:9$$

Solution

$$\dfrac{V_{1}}{V_{2}}=\dfrac{64}{27}$$ [$$V_{1}, V_{2}$$ are the volumes of two spheres]
$$\Rightarrow \dfrac{\frac{4}{3}\pi r_{1}^{3}}{\dfrac{4}{3}\pi r_{2}^{3}}=\dfrac{64}{27}$$ [$$r_{1}, r_{2}$$ are the radii of two spheres]
$$\Rightarrow \left ( \dfrac{r_{1}}{r_{2}} \right )^{3}=\left ( \dfrac{4}{3} \right )^{3}$$
$$\Rightarrow \dfrac{r_{1}}{r_{2}}=\dfrac{4}{3}$$
Now, the ratio of their surface areas is given by
$$\dfrac{T,S.A_{1}}{T.S.A_{2}}=\dfrac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}=\left ( \dfrac{r_{1}}{r_{2}} \right )^{2}=\left ( \dfrac{4}{3} \right )^{2}=\dfrac{16}{9}$$
Hence, the required ratio $$16 : 9$$ verifies the given option.
Question 5
1 / -0

The surface area of a sphere of radius $$7$$ cm is:

A
$$88 cm^2$$

B
$$616 cm^2$$

C
$$661 cm^2$$

D
$$308 cm^2$$

Solution

We know,
Surface area of sphere, $$A= 4 \pi r^2$$, where $$r$$ is the radius of sphere.
Here, $$r=7\ cm $$
Therefore, $$A=4\times \dfrac{22} 7 \times 7 \times 7=616\ cm^2$$.
Hence, option $$B$$ is correct.
Question 6
1 / -0

If the diameter of a sphere is d, then it's volume is

A
$$\frac{1}{3} \pi d^3$$

B
$$\frac{1}{24} \pi d^3$$

C
$$\frac{4}{3} \pi d^3$$

D
$$\frac{1}{6} \pi d^3$$

Solution

If the diameter of a sphere is d, then it's volume is $$\frac{1}{6} \pi d^3$$
Question 7
1 / -0

The ratio of the radii of two spheres is $$4:5$$. Find the ratio of their total surface areas is:

A
$$5 : 4$$

B
$$4 : 5$$

C
$$16 : 25$$

D
$$25 : 16$$

Solution

Given, the ratio of radii of two spheres is $$4:5$$.
We know, the surface area of a sphere $$=4 \pi r^2$$.

Let $$r_1$$ and $$r_2$$ be the radii of the two sphere,
i.e. $$r_1 : r_2=4:5=\dfrac{4}{5}$$.

Then, the areas of the spheres be $$4 \pi r_1^2$$ and $$4 \pi r_2^2$$.

Therefore, the ratio of their surface area
$$=\dfrac{4 \pi r_1^2}{4\pi r_2^2}\\=\dfrac{r_1^2}{r_2^2}\\=(\dfrac{r_1}{r_2})^2\\=(\dfrac{4}{5})^2\\=\dfrac{16}{25}\\=16:25$$.

Hence, option $$C$$ is correct.
Question 8
1 / -0

If the diameter of a sphere is 'd' then its volume is:

A
$$\frac{1}{3} \pi d^3$$

B
$$\frac{1}{2} \pi d^3$$

C
$$\frac{4}{3} \pi d^3$$

D
$$\frac{1}{6} \pi d^3$$

Solution

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 = $$\dfrac{4}{3}\pi \left(\dfrac{d}{2}\right )^3 $$= $$\dfrac{1}{6} \pi d^3$$
Question 9
1 / -0

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 $$729:1$$.

A
$$27:1$$

B
$$81:1$$

C
$$19,683:1$$

D
$$26,224:1$$

E
$$531,441:1$$

Solution

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 $$\dfrac { \frac { 4 }{ 3 } \pi { a }^{ 3 } }{ \frac { 4 }{ 3 } \pi { b }^{ 3 } } $$

$$=\left (\dfrac {a}{b}\right)^3={ 27 }^{ 3 }$$

$$=19683$$
Question 10
1 / -0

A hemispherical tank full of water is emptied by a pipe at the rate of $$\displaystyle {3}\frac{4}{7}$$ litres per second . How much time will it take to half empty the tank, if the tank is $$3$$ metres in diameter? (Take $$\pi = \dfrac{22}{7})$$

A
$$16.5$$ min.

B
$$12.8$$ min.

C
$$20.5$$ min.

D
$$18.2$$ min.

Solution

Radius of the hemispherical tank $$ = \dfrac {3}{2} = 1.5 $$ m
Volume of a hemisphere of radius '$$r$$' $$ = \dfrac { 2 }{ 3 } \pi r^3$$
Hence, volume of the tank $$ = \dfrac {2}{3} \times \dfrac {22}{7} \times \dfrac {3}{2} \times \dfrac {3}{2} \times \dfrac {3}{2} = \dfrac {99}{14} {m}^{3} $$
Half of the volume of the tank $$ = \dfrac {99}{28} \text{m}^{3} =\dfrac {99}{28} \times 1000 $$ litres
To empty, $$ 3 \dfrac {4}{7} = \dfrac {25}{7} $$ litres, time is one second
To empty $$ \dfrac {99}{28} \times 1000 $$ litres, time $$ = \dfrac { \frac {99}{28} \times 1000}{ \frac {25}{7}} = 990 $$ seconds $$= 16.5 $$ min

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 50

Result

Surface Areas and Volumes Test - 50

Score

-

Rank

-

SHARING IS CARING

Question 1

$$1:8$$

$$1:4$$

$$1:27$$

$$8:1$$

Solution

Question 2

$$84\ cm^2$$

$$124\ cm^2$$

$$164\ cm^2$$

$$180\ cm^2$$

Solution

Question 3

$$390\ cm^2$$

$$1390\ cm^2$$

$$2780\ cm^2$$

$$1000\ cm^2$$

Solution

Question 4

$$3:4$$

$$4:3$$

$$9:16$$

$$16:9$$

Solution

Question 5

$$88 cm^2$$

$$616 cm^2$$

$$661 cm^2$$

$$308 cm^2$$

Solution

Question 6

$$\frac{1}{3} \pi d^3$$

$$\frac{1}{24} \pi d^3$$

$$\frac{4}{3} \pi d^3$$

$$\frac{1}{6} \pi d^3$$

Solution

Question 7

$$5 : 4$$

$$4 : 5$$

$$16 : 25$$

$$25 : 16$$

Solution

Question 8

$$\frac{1}{3} \pi d^3$$

$$\frac{1}{2} \pi d^3$$

$$\frac{4}{3} \pi d^3$$

$$\frac{1}{6} \pi d^3$$

Solution

Question 9

$$27:1$$

$$81:1$$

$$19,683:1$$

$$26,224:1$$

$$531,441:1$$

Solution

Question 10

$$16.5$$ min.

$$12.8$$ min.

$$20.5$$ min.

$$18.2$$ min.

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.