Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 34

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Weekly Quiz Competition

Question 1
1 / -0

What is the volume of the cuboid of the brick? (Given : length $$= 23$$ cm, breadth $$= 10$$ cm, height $$= 12$$ cm)

A
$$\displaystyle 2765{ cm }^{ 3 }$$

B
$$\displaystyle 2760{ cm }^{ 3 }$$

C
$$\displaystyle 2340{ cm }^{ 3 }$$

D
$$\displaystyle 2901{ cm }^{ 3 }$$

Solution

$$Volume\ of\ cuboid=length\times breadth\times height$$
$$length=223\ cm$$
$$breadth=10\ cm$$
$$height=12\ cm$$
$$volume=23\times 10\times 12=2760\ cm^3$$
Question 2
1 / -0

Find the volume of this rectangular prism (cuboid). $$($$Given: $$L = 2$$ cm, $$B = 10$$ cm, $$H = 30$$ cm$$)$$

A
$$\displaystyle 600\ { cm }^{ 3 }$$

B
$$\displaystyle 760\ { cm }^{ 3 }$$

C
$$\displaystyle 42\ { cm }^{ 3 }$$

D
$$\displaystyle 500\ { cm }^{ 3 }$$

Solution

Volume of the cuboid $$=$$ length $$\times$$ breadth $$\times$$ height
Therefore, length $$= 2$$ cm, breadth $$= 10$$ cm, height $$= 30$$ cm
Volume of the cuboid $$=$$ $$\displaystyle 2\times 10\times 30=600{ cm }^{ 3 }$$
Question 3
1 / -0

A plastic box $$3.5$$ m long, $$2$$ m wide and $$20$$ m deep is to be made. Find its volume.

A
$$\displaystyle 160\ { m }^{ 3 }$$

B
$$\displaystyle 70\ { m }^{ 3 }$$

C
$$\displaystyle 140\ { m }^{ 3 }$$

D
$$\displaystyle 50\ { m }^{ 3 }$$

Solution

Volume of the plastic box $$=$$ length $$\times $$ breadth $$\times$$ height
Therefore, length $$= 2$$ m, breadth $$= 20$$ m, height $$= 3.5$$ m
Therefore, volume $$=$$ $$\displaystyle 2\times 20\times 3.5=140{ m }^{ 3 }$$
Question 4
1 / -0

If the side of cube is $$2\text{ m}$$, then surface area of cube is

A
$$24\:\text{m}^2$$

B
$$124\:\text{m}^2$$

C
$$24\:\text{m}$$

D
$$124\:\text{m}$$

Solution

Given, side of a cube $$=2\text{ m}$$
Let $$'a'$$ be the length of the side of the cube.
Surface area of the cube $$=$$ $$6 \times a^2$$
$$= 6 \times 2^2$$
$$=6 \times 4$$
$$=24 \text{ m}^2$$
So, option A is correct.
Question 5
1 / -0

If $$s$$ represents the side, then the formula of surface area of cube is

A
$$6(s)^2$$

B
$$3(s)^2$$

C
$$5(s)^2$$

D
$$16(s)^2$$

Solution

Side of the cube $$=$$ $$s$$
Area of $$1$$ surface of cube $$=s \times s = s^2$$
A cube has $$6$$ surfaces.
$$\therefore \mbox{Total surface area of cube = }$$$$6 \times \mbox{Area of 1 surface}$$ $$=6s^2$$
So, option A is correct.
Question 6
1 / -0

The side of a cube 4 cm. Its area is---

A
16 sq. cm

B
64 sq. cm

C
12 sq. cm

D
None of these

Solution

TSA of a cube $$= 4$$ $$\times \,\, (Side)^2$$
$$= 4$$ $$\times \,\, (4)^2$$ sq. cm
$$= 4$$ $$\times$$ 16 sq. cm
$$= 64$$ sq. cm
Question 7
1 / -0

Capacity is not measured in ..........

A
Litres

B
Millilitres

C
Cubic centimetres

D
Centimetres

Solution
Question 8
1 / -0

Find the total surface area of the given cuboid.

A
$$\displaystyle 130{ m }^{ 2 }$$

B
$$\displaystyle 131{ m }^{ 2 }$$

C
$$\displaystyle 132{ m }^{ 2 }$$

D
$$\displaystyle 133{ m }^{ 2 }$$

Solution

Given, length $$(l)=8\ m$$
breadth $$(b)=5\ m$$
height $$(h)=2\ m$$

Surface area of the cuboid $$\displaystyle =2\times \left( lb+lh+bh \right) $$

$$\displaystyle =2\times \left( 8\times 5+8\times 2+5\times 2 \right) \ m^2$$

$$\displaystyle =2\times \left( 40+16+10 \right) \ m^2$$

$$\displaystyle =2\times 66\ m^2$$

$$\displaystyle =132\ { m }^{ 2 }$$

Hence, total surface area is $$132\ { m }^{ 2 }$$
Question 9
1 / -0

Kyle bought 2 snack boxes. Box A has a measure of $$2\ in\times 3\ in\times 5 \ in.$$ Box B has a measure of $$11 \ in\times 4\ in \times 3\ in.$$ Find the surface area of the boxes and their difference.

A
$$\displaystyle 116{ in }^{ 2 }$$

B
$$\displaystyle 201{ in }^{ 2 }$$

C
$$\displaystyle 279{ in }^{ 2 }$$

D
$$\displaystyle 198{in }^{ 2 }$$

Solution

Surface area of rectangle is 2 x (Length x width + Length x height + Width x height)

Here Box A has length $$= 2$$ in, height $$= 3$$ in and width $$= 5$$ in

Therefore, the surface area of Box A is:

$$A=2((2\times 5)+(2\times 3)+(3\times 5))=2(10+6+15)=2\times 31=62$$ in$$^2$$

Now, Box B has length $$= 11$$ in, height $$= 4$$ in and width $$= 3$$ in

Therefore, the surface area of Box B is:

$$A=2((11\times 4)+(11\times 3)+(4\times 3))=2(44+33+12)=2\times 89=178$$ in$$^2$$

Hence, the difference between the surface area of box A and box B is $$178-62=116$$ in$$^2$$.
Question 10
1 / -0

What is the surface area of a television $$20$$ inches long, $$15$$ inches wide and $$5$$ inches high?

A
$$\displaystyle 980{\ in }^{ 2 }$$

B
$$\displaystyle 950{ \ in }^{ 2 }$$

C
$$\displaystyle 915{\ in }^{ 2 }$$

D
$$\displaystyle 925{\ in }^{ 2 }$$

Solution

Surface area$$ = 2 ($$Length $$\times$$ width $$+$$ Length $$\times$$ height $$+$$ Width $$\times$$ height$$)$$
Length $$= 20$$ in; Height $$= 5$$ in; Width $$= 15$$ in
$$\displaystyle = 2\times \left( 20\times 15+20\times 5+15\times 5 \right) $$
$$\displaystyle = 2\times \left( 300+100+75 \right) $$
$$\displaystyle = 2\times 475$$
$$\displaystyle = 950{\ in }^{ 2 }$$

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Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 34

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Surface Areas and Volumes Test - 34

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SHARING IS CARING

Question 1

$$\displaystyle 2765{ cm }^{ 3 }$$

$$\displaystyle 2760{ cm }^{ 3 }$$

$$\displaystyle 2340{ cm }^{ 3 }$$

$$\displaystyle 2901{ cm }^{ 3 }$$

Solution

Question 2

$$\displaystyle 600\ { cm }^{ 3 }$$

$$\displaystyle 760\ { cm }^{ 3 }$$

$$\displaystyle 42\ { cm }^{ 3 }$$

$$\displaystyle 500\ { cm }^{ 3 }$$

Solution

Question 3

$$\displaystyle 160\ { m }^{ 3 }$$

$$\displaystyle 70\ { m }^{ 3 }$$

$$\displaystyle 140\ { m }^{ 3 }$$

$$\displaystyle 50\ { m }^{ 3 }$$

Solution

Question 4

$$24\:\text{m}^2$$

$$124\:\text{m}^2$$

$$24\:\text{m}$$

$$124\:\text{m}$$

Solution

Question 5

$$6(s)^2$$

$$3(s)^2$$

$$5(s)^2$$

$$16(s)^2$$

Solution

Question 6

16 sq. cm

64 sq. cm

12 sq. cm

None of these

Solution

Question 7

Litres

Millilitres

Cubic centimetres

Centimetres

Solution

Question 8

$$\displaystyle 130{ m }^{ 2 }$$

$$\displaystyle 131{ m }^{ 2 }$$

$$\displaystyle 132{ m }^{ 2 }$$

$$\displaystyle 133{ m }^{ 2 }$$

Solution

Question 9

$$\displaystyle 116{ in }^{ 2 }$$

$$\displaystyle 201{ in }^{ 2 }$$

$$\displaystyle 279{ in }^{ 2 }$$

$$\displaystyle 198{in }^{ 2 }$$

Solution

Question 10

$$\displaystyle 980{\ in }^{ 2 }$$

$$\displaystyle 950{ \ in }^{ 2 }$$

$$\displaystyle 915{\ in }^{ 2 }$$

$$\displaystyle 925{\ in }^{ 2 }$$

Solution

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