Mensuration Test

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Mensuration Test - 24

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Weekly Quiz Competition

Question 1
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
$$\displaystyle = 2\times \left( 20\times 15+20\times 5+15\times 5 \right) $$
$$\displaystyle = 2\times \left( 300+100+75 \right) $$
$$\displaystyle = 2\times 475$$
$$\displaystyle = 950{\ in }^{ 2 }$$
Question 2
1 / -0

Length, breadth and height of a room are $$12$$ ft, $$5$$ ft and $$8$$ ft respectively. Find the volume of the room.

A
$$\displaystyle 440{ ft }^{ 3 }$$

B
$$\displaystyle 480{ ft }^{ 3 }$$

C
$$\displaystyle 400{ ft }^{ 3 }$$

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

Solution

Length of the room $$= 12$$ ft
Breadth of the room $$= 5$$ ft
Height of the room $$= 8$$ ft
Therefore, volume of the room $$=$$ length $$\times$$ breadth $$\times$$ height
$$\displaystyle =12\times 5\times 8{ ft }^{ 3 }$$
$$\displaystyle =480$$ $${ ft }^{ 3 }$$
Question 3
1 / -0

Find the surface area of a cuboid:

A
$$\displaystyle 110$$ unit $$^{ 2 }$$

B
$$\displaystyle 120$$ unit $$^{ 2 }$$

C
$$\displaystyle 130$$ unit $$^{ 2 }$$

D
$$\displaystyle 140$$ unit $$^{ 2 }$$

Solution

Surface area $$= 2 ($$Length $$\times$$ width $$+$$ Length $$\times$$ height $$+$$ Width $$\times$$ height$$)$$

Length $$= 5$$ units; Height $$= 5$$ units; Width $$= 4$$ units

$$\displaystyle =2\times \left( 5\times 4+5\times 5+4\times 5 \right) $$

$$\displaystyle =2\times \left( 20+25+20 \right) $$

$$\displaystyle =2\times 65$$

$$\displaystyle= 130$$ unit $$^{ 2 }$$
Question 4
1 / -0

A parcel has to be packed with length $$1$$ m, width $$0.1$$ m and height $$0.05$$ m. Find the volume of the parcel in cubic cm.

A
$$\displaystyle { 6050\ cm }^{ 3 }$$

B
$$\displaystyle { 7000\ cm }^{ 3 }$$

C
$$\displaystyle { 5000\ cm }^{ 3 }$$

D
$$\displaystyle { 1300\ cm }^{ 3 }$$

Solution

Given dimensions of the parcel are, length $$= 1$$ m or $$100$$ cm, width $$= 0.1$$ m or $$10$$ cm and height $$= 0.05$$ m or $$5$$ cm
Therefore, volume of the parcel $$=$$ length $$\times$$ width $$\times$$ height
$$\displaystyle =\left( 100\times 10\times 5 \right) { cm }^{ 3 }$$
$$\displaystyle =5000{\ cm }^{ 3 }$$
Question 5
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 6
1 / -0

Find the total surface area of a cuboid given $$l =10\ cm,$$ $$h = 4\ cm$$ and $$w = 13\ cm$$.

A
$$444{ \ cm }^{ 2 }$$

B
$$222{\ cm }^{ 2 }$$

C
$$333{ \ cm }^{ 2 }$$

D
$$111{ \ cm }^{ 2 }$$

Solution

$$\begin{aligned}{}{\text{Area}} &= 2(lw + wh + hl)\\ &= 2 \left( {10 \times 13 + 13 \times 4 + 4 \times 10} \right)\\& = 2 \left( {130 + 52 + 40} \right)\\& = 2 \times 222\\ &= 444\ c{m^2}\end{aligned}$$
Question 7
1 / -0

Find the surface area of a cuboid with dimensions $$ 4 \times 2.5 \times 2$$ (in inches)

A
$$\displaystyle 46{ \text{ in.} }^{ 2 }$$

B
$$\displaystyle 12{\text{ in.} }^{ 2 }$$

C
$$\displaystyle 26\text{ in.}^{ 2 }$$

D
$$\displaystyle 14{\text{ in.} }^{ 2 }$$

Solution

According to the given dimensions let,
$$l=4\text{ in.}$$
$$w=2.5\text{ in.}$$
$$h=2\text{ in.}$$

By using the formula of total surface area of a cuboid we get,
$$\begin{aligned}{}{\rm{Area}} &= 2(lw + wh + hl)\\ &= 2\left( {4 \times 2.5 + 2.5 \times 2 + 4 \times 2} \right)\\ &= 2\left( {10 + 5 + 8} \right)\\ &= 2 \times 23\\ &= 46\text{ in.}^2\end{aligned}$$
Question 8
1 / -0

Find the volume of a cuboid whose length is $$100\ m,$$ breadth is $$0.2\ m$$ and height is $$0.15\ m.$$

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

B
$$1.25\ { m }^{ 3 }$$

C
$$4\ { m }^{ 3 }$$

D
$$5\ { m }^{ 3 }$$

Solution

Volume of the cuboid whose length is $$l,$$ breadth is $$b$$ and height is $$h$$ is given by,
$$V=l\times b\times h$$

Given:
$$l= 100\ m$$
$$b= 0.2\ m$$
$$h= 0.15\ m$$

So,
$$V=100\times 0.2\times 0.15$$
$$=20\times 0.15$$
$$=3\ m^3$$

Hence, option $$A$$ is correct.
Question 9
1 / -0

Find the volume of the cuboid having length, breadth and height as $$12$$ cm, $$15$$ cm and $$30$$ cm.

A
$$\displaystyle 6000{ cm }^{ 3 }$$

B
$$\displaystyle 5400{ cm }^{ 3 }$$

C
$$\displaystyle 4200{ cm }^{ 3 }$$

D
$$\displaystyle 5000{ cm }^{ 3 }$$

Solution

Volume of the cuboid $$=$$ length $$\times$$ breadth $$\times$$ height
Therefore, length $$= 12$$ cm, breadth $$= 15$$ cm, height $$= 30$$ cm
Volume of the cuboid $$\displaystyle \\ = 12\times 15\times 30=5400{ cm }^{ 3 }\\ $$
Question 10
1 / -0

Michael has a box measured $$2.1$$ meters in length, $$1.9$$ meters in height and $$2.5$$ meters in width. What is the surface area of his box can hold?

A
$$\displaystyle 18.21{ m }^{ 2 }$$

B
$$\displaystyle 20.21{ m }^{ 2 }$$

C
$$\displaystyle 27.98{ m }^{ 2 }$$

D
$$\displaystyle 18.08{ m }^{ 2 }$$

Solution

Surface area $$=$$ $$2 \times$$ $$($$Length $$\times$$ width $$+$$ Length $$\times$$ height $$+$$ Width $$\times$$ height$$)$$
Length $$= 2.1$$ m; Height $$= 1.9$$ m; Width $$= 2.5$$ m
$$\displaystyle =2\times \left( 5.25+3.99+4.75 \right) $$
$$\displaystyle =2\times 13.99$$
$$\displaystyle =27.98$$ $${ m }^{ 2 }$$

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Re-Attempt Weekly Quiz Competition

Mensuration Test - 24

Result

Mensuration Test - 24

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SHARING IS CARING

Question 1

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

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

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

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

Solution

Question 2

$$\displaystyle 440{ ft }^{ 3 }$$

$$\displaystyle 480{ ft }^{ 3 }$$

$$\displaystyle 400{ ft }^{ 3 }$$

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

Solution

Question 3

$$\displaystyle 110$$ unit $$^{ 2 }$$

$$\displaystyle 120$$ unit $$^{ 2 }$$

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

$$\displaystyle 140$$ unit $$^{ 2 }$$

Solution

Question 4

$$\displaystyle { 6050\ cm }^{ 3 }$$

$$\displaystyle { 7000\ cm }^{ 3 }$$

$$\displaystyle { 5000\ cm }^{ 3 }$$

$$\displaystyle { 1300\ cm }^{ 3 }$$

Solution

Question 5

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

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

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

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

Solution

Question 6

$$444{ \ cm }^{ 2 }$$

$$222{\ cm }^{ 2 }$$

$$333{ \ cm }^{ 2 }$$

$$111{ \ cm }^{ 2 }$$

Solution

Question 7

$$\displaystyle 46{ \text{ in.} }^{ 2 }$$

$$\displaystyle 12{\text{ in.} }^{ 2 }$$

$$\displaystyle 26\text{ in.}^{ 2 }$$

$$\displaystyle 14{\text{ in.} }^{ 2 }$$

Solution

Question 8

$$3\ { m }^{ 3 }$$

$$1.25\ { m }^{ 3 }$$

$$4\ { m }^{ 3 }$$

$$5\ { m }^{ 3 }$$

Solution

Question 9

$$\displaystyle 6000{ cm }^{ 3 }$$

$$\displaystyle 5400{ cm }^{ 3 }$$

$$\displaystyle 4200{ cm }^{ 3 }$$

$$\displaystyle 5000{ cm }^{ 3 }$$

Solution

Question 10

$$\displaystyle 18.21{ m }^{ 2 }$$

$$\displaystyle 20.21{ m }^{ 2 }$$

$$\displaystyle 27.98{ m }^{ 2 }$$

$$\displaystyle 18.08{ m }^{ 2 }$$

Solution

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