Surface Areas and Volumes Test

Result

Surface Areas and Volumes Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

The total surface area of a solid hemisphere of radius $$r$$ is given by

A
$$2\pi r^2$$

B
$$\pi r^2$$

C
$$3\pi r^2$$

D
$$4\pi r^2$$

Solution

Curved surface area of hollow hemisphere $$=2\pi r^2$$
The area of a circlular base of radius $$r$$ is $$\pi {{r}^{2}}$$ .
Total surface area of solid hemisphere $$2\pi {{r}^{2}}+\pi {{r}^{2}}=3\pi {{r}^{2}}$$ .
Question 2
1 / -0

A reservoir is 3 m long, 2 m wide and 1 deep. Its capacity in litres is

A
8000 litres

B
10000 litres

C
6500 litres

D
6000 litres

Solution

Volume of the reservoir = l x b x h=3 x 2 x 1=6 cu m
$$\displaystyle \left ( \because 1 cu\, m = 1000 litre \right )$$
($$\displaystyle \because $$ Capacity of the reservoir =6 x 1000 =6000 litre.
Question 3
1 / -0

The diameter of a sphere is 21 cm. Calculate its volume

A
4851 $$\displaystyle cm^{3}$$

B
4000 $$\displaystyle cm^{3}$$

C
2000 $$\displaystyle cm^{3}$$

D
3850 $$\displaystyle cm^{3}$$

Solution

Diameter = 21 cm
$$\displaystyle r=\dfrac{21}{2}cm$$
Volume of the sphere$$\displaystyle =\dfrac{4}{3}\pi r^{3}$$
$$\displaystyle =\dfrac{4}{3}\times \dfrac{22}{7}\times \dfrac{21}{2}\times \dfrac{21}{2}\times \dfrac{21}{2}$$
$$\displaystyle= 4851 cm^{3}$$
Question 4
1 / -0

The radius of a sphere is 3 cm. Its volume is:

A
113.14 $$\displaystyle cm^{3}$$

B
120 $$\displaystyle cm^{3}$$

C
108 $$\displaystyle cm^{3}$$

D
112.12 $$\displaystyle cm^{3}$$

Solution

Volume of sphere $$\displaystyle =\dfrac{4}{3}\pi r^{3}$$

$$=\dfrac{4}{3}\times \dfrac{22}{7}\times \left ( 3 \right )^{3}$$

$$=113.14cm^{3}$$
Question 5
1 / -0

A solid in the form of a cuboid is 4 cm x 3 cm x 2 cm. Its volume will be
(Note: cu cm $$=cm^3$$)

A
20 cu cm

B
22 cu cm

C
28 cu cm

D
24 cu cm

Solution

Volume of the cuboid =$$l$$ x$$ b$$ x$$ h$$ =$$4$$ x$$ 3$$ x$$ 2$$
$$ =24$$ cu cm
Question 6
1 / -0

The curved surface area of a hemisphere of diameter $$2 r$$ is:

A
$$\displaystyle 2\pi r^{2}$$

B
$$\displaystyle 3\pi r^{2}$$

C
$$\displaystyle 4\pi r^{2}$$

D
$$\displaystyle 8\pi r^{2}$$

Solution

Diameter of the hemisphere= $$2r$$
$$\therefore \text{Radius}=\dfrac{2r}{2}=r \ \text{cm}$$
Curved surface area of hemisphere$$=2 \pi r^2$$
Question 7
1 / -0

If the surface area of a sphere is $$ \displaystyle 324\pi cm^{2} $$ then its volume is

A
$$ \displaystyle 950 \pi $$ $$\displaystyle cm^{3}$$

B
$$ \displaystyle 972 \pi $$ $$\displaystyle cm^{3}$$

C
$$ \displaystyle 975 \pi $$ $$\displaystyle cm^{3}$$

D
$$ \displaystyle 980\pi $$ $$\displaystyle cm^{3}$$

Solution

Given the surface area of sphere is $$324\pi cm^{2}$$
$$\therefore 4\pi r^{2}=324\pi \Rightarrow r^{2}=81\Rightarrow r=9$$ cm
then volume of sphere=$$\frac{4}{3}\pi (9)^{3}=\frac{4}{3}\times \pi \times 729=972\pi cm^{3}$$
Question 8
1 / -0

If the volume in $$ \displaystyle m ^{2} $$ and the surface area in $$ \displaystyle m ^{2} $$ of a sphere are numerically equal then the radius of the sphere in m is

A
4

B
2

C
3.5

D
3

Solution

Let the radius of the sphere is m
So volume of sphere=$$\frac{4}{3}\pi m^{3}$$
And surface area of sphere= $$4\pi m^{2}$$
As per question both are numerically equal
$$\therefore \frac{4}{3}\pi m^{3}=\pi m^{2}\Rightarrow m=3$$
Question 9
1 / -0

$$l \times b \times h$$ is formula of---

A
Area of cube

B
Area of cuboid

C
Volume of a cuboid

D
None of these

Solution

Correct answer is C.
Question 10
1 / -0

A toy box can fit $$36$$ equal sized unit blocks in it. Then its volume is

A
$$36\,sq\,units$$

B
$$63\,sq\,units$$

C
$$36\,cu\,units$$

D
$$62\,cu\,units$$

Solution

$$\Rightarrow$$ Length of any edge of toy box $$(l)=1\,unit$$

$$\Rightarrow$$ Volume of $$1$$ toy box $$=(l)^3$$
$$=1\,cu\,units$$

$$\Rightarrow$$ Volume of $$36$$ equal sized toy box $$=36\times 1\,cu\,units$$
$$=36\,cu\,units$$.

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 18

Result

Surface Areas and Volumes Test - 18

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SHARING IS CARING

Question 1

$$2\pi r^2$$

$$\pi r^2$$

$$3\pi r^2$$

$$4\pi r^2$$

Solution

Question 2

8000 litres

10000 litres

6500 litres

6000 litres

Solution

Question 3

4851 $$\displaystyle cm^{3}$$

4000 $$\displaystyle cm^{3}$$

2000 $$\displaystyle cm^{3}$$

3850 $$\displaystyle cm^{3}$$

Solution

Question 4

113.14 $$\displaystyle cm^{3}$$

120 $$\displaystyle cm^{3}$$

108 $$\displaystyle cm^{3}$$

112.12 $$\displaystyle cm^{3}$$

Solution

Question 5

20 cu cm

22 cu cm

28 cu cm

24 cu cm

Solution

Question 6

$$\displaystyle 2\pi r^{2}$$

$$\displaystyle 3\pi r^{2}$$

$$\displaystyle 4\pi r^{2}$$

$$\displaystyle 8\pi r^{2}$$

Solution

Question 7

$$ \displaystyle 950 \pi $$ $$\displaystyle cm^{3}$$

$$ \displaystyle 972 \pi $$ $$\displaystyle cm^{3}$$

$$ \displaystyle 975 \pi $$ $$\displaystyle cm^{3}$$

$$ \displaystyle 980\pi $$ $$\displaystyle cm^{3}$$

Solution

Question 8

4

2

3.5

3

Solution

Question 9

Area of cube

Area of cuboid

Volume of a cuboid

None of these

Solution

Question 10

$$36\,sq\,units$$

$$63\,sq\,units$$

$$36\,cu\,units$$

$$62\,cu\,units$$

Solution

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