Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

2(lb + bh + hl) is formula of---

A
Area of a cuboid

B
Area of a cube

C
Volume of a cuboid

D
None of these

Solution

The correct option is A.
Question 2
1 / -0

If the radius of a sphere is doubled then the volume of a sphere becomes

A
doubled

B
six times

C
four times

D
eight times

Solution

Let the radius of sphere is r
Then volume of sphere =$$\frac{4}{3}\pi r^{3}$$
If radius of sphere is doubled then radius is 2r
Then volume of new sphere =$$\frac{4}{3}\pi (2r)^{3}=\frac{4}{3}\times 8r^{3}$$
Then ratio of new and old sphere=$$\frac{\frac{4}{3}\times 8r^{3}}{\frac{4}{3}r^{3}}=\frac{8}{1}$$
Then the radius of sphere is doubled then volume become eight times
Question 3
1 / -0

Find the volume of the sphere whose diameter is 30 cm.

A
1.41428 cm$$\displaystyle ^{3}$$

B
1414.28 cm$$\displaystyle ^{3}$$

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

D
14142.8 cm$$\displaystyle ^{3}$$

Solution

Given: Diameter $$= 30 cm$$
$$\displaystyle \therefore Radius = \frac{30}{2}= 15 cm $$
$$\displaystyle \therefore\ Volume\ of\ the\ sphere =\frac{4}{3}\pi r^{3}=\frac{4}{3}\times \frac{22}{7}\times 15\times 15\times 15=14142.8 5cm^{3}$$
Question 4
1 / -0

Volume of a cuboid with $$l = 10 cm, b = 12 cm, h = 8 cm$$ is

A
$$96$$ cubic cm

B
$$9.6$$ cubic cm

C
$$9600$$ cubic cm

D
$$960$$ cubic cm

Solution

$$\Rightarrow$$ $$l=10\,cm,\,b=12\,cm$$ and $$h=8\,cm$$ [ Given ]

$$\Rightarrow$$ Volume of a cuboid $$=l\times b\times h$$

$$=10cm\times 12cm\times 8cm$$

$$=960\,cm^3$$
Question 5
1 / -0

What is the total surface area of a cuboid ?

A
$$2(lb + bh + hl)$$

B
$$(l \times b \times h)$$

C
$$(l \times b)$$

D
None of these

Solution

Let the length, breadth and height of the cuboid be $$l,\ b$$ and $$h$$ respectively.

The total surface area of a cuboid (TSA) is equal to the sum of the areas of its 6 rectangular faces.

TSA of cuboid $$=l\times b+b\times h+h\times l+l\times b+b\times h+h\times l$$

$$=2(lb + bh + hl)$$
Question 6
1 / -0

Find the volume of a sphere of radius given below:

A
$$\displaystyle 1,706.25{ \ ft }^{ 3 }$$

B
$$\displaystyle 1,766.15{\ ft }^{ 3 }$$

C
$$\displaystyle 1,866.25{\ ft }^{ 3 }$$

D
$$\displaystyle 1,766.25{\ ft }^{ 3 }$$

Solution

Using formula volume of sphere =$$\dfrac{4}{3} \pi r^3$$
$$r=radius$$
Given: $$radius(r)=7.5\ ft$$
$$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}\times 3.14 \times 7.5^3$$
$$=\dfrac{4}{3} \times 7.5 \times 7.5 \times 7.5 \times 3.14$$
$$=\dfrac{4}{3} \times 421.875 \times 3.14$$
$$=\dfrac{5298.75}{3}$$
$$=1766.25\ ft^3$$
Question 7
1 / -0

Volume of a suitcase with clothes in it is ................... the volume of empty suitcase. (Both suitcases are of same size)

A
more than

B
less than

C
equal to

D
none of these

Solution

Whether the volume of the suitcase is occupied or not the volume will remain the same. So the volume of the same suitcase whether it haves clothes in it or not will remain equal.
So option C is the correct answer.
Question 8
1 / -0

The total surface area of a cube is ____ .

A
$$\displaystyle 3{ a }^{ 2 }$$

B
$$\displaystyle 6{ a }^{ 2 }$$

C
$$\displaystyle 4{ a }^{ 2 }$$

D
$$\displaystyle 5{ a }^{ 2 }$$

Solution

A cube has all edges of the same length. This means that each of the cube's six faces is a square. The total surface area is therefore six times the area of one face $$\displaystyle 6{ a }^{ 2 }$$ where $$a$$ is edge length of the cube.
Question 9
1 / -0

Lateral surface area of a cylinder is

A
$$2\pi r^2$$

B
$$2\pi rh^2$$

C
$$2\pi rh$$

D
None

Solution

Area of lateral surface of cylinder $$=$$ Curved surface of cylinder
Curved surface of cylinder $$=$$ Circumference of circular base $$ \times $$ height
Therefore, lateral surface area of a cylinder $$=2 \pi r h$$
Question 10
1 / -0

Fill in the blanks:
Surface area of a cylinder = ............. x ........... + .......... .

A
2 $$\times$$ area of rectangle $$+$$ area of circle

B
2 $$\times$$ area of circle $$+$$ area of rectangle

C
2 $$\times$$ area of square $$+$$ area of rectangle

D
2 $$\times$$ area of rectangle $$+$$ area of rectangle

Solution

Cylinder is made up of $$2$$ circles and one rectangle as shown in the figure.
Length of the rectangle is the circumference of circle. Breadth will be height of cylinder.
Hence cylinder is the addition of two areas of circle and one rectangle.
So, option (b) is correct.

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Surface Areas and Volumes Test - 19

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Surface Areas and Volumes Test - 19

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Question 1

Area of a cuboid

Area of a cube

Volume of a cuboid

None of these

Solution

Question 2

doubled

six times

four times

eight times

Solution

Question 3

1.41428 cm$$\displaystyle ^{3}$$

1414.28 cm$$\displaystyle ^{3}$$

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

14142.8 cm$$\displaystyle ^{3}$$

Solution

Question 4

$$96$$ cubic cm

$$9.6$$ cubic cm

$$9600$$ cubic cm

$$960$$ cubic cm

Solution

Question 5

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

$$(l \times b \times h)$$

$$(l \times b)$$

None of these

Solution

Question 6

$$\displaystyle 1,706.25{ \ ft }^{ 3 }$$

$$\displaystyle 1,766.15{\ ft }^{ 3 }$$

$$\displaystyle 1,866.25{\ ft }^{ 3 }$$

$$\displaystyle 1,766.25{\ ft }^{ 3 }$$

Solution

Question 7

more than

less than

equal to

none of these

Solution

Question 8

$$\displaystyle 3{ a }^{ 2 }$$

$$\displaystyle 6{ a }^{ 2 }$$

$$\displaystyle 4{ a }^{ 2 }$$

$$\displaystyle 5{ a }^{ 2 }$$

Solution

Question 9

$$2\pi r^2$$

$$2\pi rh^2$$

$$2\pi rh$$

None

Solution

Question 10

2 $$\times$$ area of rectangle $$+$$ area of circle

2 $$\times$$ area of circle $$+$$ area of rectangle

2 $$\times$$ area of square $$+$$ area of rectangle

2 $$\times$$ area of rectangle $$+$$ area of rectangle

Solution

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