Mensuration Test

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Mensuration Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

Find the area of the curved surface of a cylindrical box with radius 12 inches and height 20 inches.

A
$$\displaystyle 1505.1{ in }^{ 2 }$$

B
$$\displaystyle 1506.5{ in }^{ 2 }$$

C
$$\displaystyle 1507.5{ in }^{ 2 }$$

D
$$\displaystyle 1507.2{ in }^{ 2 }$$

Solution

Curved surface area of cylinder is $$A=2πrh$$

Here, the radius is $$12$$ in and height is $$20$$ in.

Thus,

$$A=2πrh=2\times 3.14\times 12\times 20=1507.2$$ in$$^2$$

Hence, the curved surface area of the cylinder is $$1507.2$$ in$$^2$$.
Question 2
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Find the surface area of the cylinder shown above:

A
$$\displaystyle 0.46\pi $$

B
$$\displaystyle 0.46\pi { m }^{ 3 }$$

C
$$\displaystyle 0.46\pi { m }^{ 2 }$$

D
$$\displaystyle 0.46\pi cm$$

Solution

Given: Radius of cylinder $$r=0.1m$$ and Height $$h=2.2m$$.
Surface area of a cylinder = $$\displaystyle 2\pi r\left( r+h \right) $$
$$\displaystyle =2\times \pi \times 0.1\left( 0.1+2.2 \right) $$
$$\displaystyle =2\times \pi \times 0.1\left( 2.3 \right) $$
$$\displaystyle =0.46\pi { m }^{ 2 }$$

So, option C is correct.
Question 3
1 / -0

Find the surface area of a cylinder:
$$r=9\ in, h=18\ in$$

A
$$\displaystyle 1526.04{\ in }^{ 2 }$$

B
$$\displaystyle 1525.03{\ in }^{ 2 }$$

C
$$\displaystyle 1526.04\ in$$

D
$$\displaystyle 1526.04{\ in }^{ 3 }$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$

Here, radius is $$r=9$$ in and the height is $$h=18$$ in.

Thus,

$$A=2πr(r+h)=2\times 3.14\times 9(9+18)=56.52\times 27=1526.04$$

Hence, the surface area of the cylinder is $$1526.04$$ in$$^2$$.
Question 4
1 / -0

The volume of a cylinder is $$616$$ cubic feet and height $$4$$ feet. Find its curved surface area. (Use $$\displaystyle \pi ={ 22 }/{ 7 }$$)

A
$$\displaystyle 88{ ft }^{ 2 }$$

B
$$\displaystyle 198{ ft }^{ 2 }$$

C
$$\displaystyle 79{ ft }^{ 2 }$$

D
$$\displaystyle 176{ ft }^{ 2 }$$

Solution

Volume of a cylinder $$=$$ $$\displaystyle \pi { r }^{ 2 }h$$

$$\Rightarrow \displaystyle 616=\frac { 22 }{ 7 } \times { r }^{ 2 }\times 4$$

$$\Rightarrow \displaystyle \frac { 616\times 7 }{ 22\times 4 } ={ r }^{ 2 }$$

$$\Rightarrow \displaystyle { r }^{ 2 }=49$$

$$\Rightarrow \displaystyle r=\sqrt { 49 } =7ft$$

Curved surface area $$=$$ $$\displaystyle 2\pi rh$$

$$\displaystyle =2\times \frac { 22 }{ 7 } \times 7\times 4$$

$$\displaystyle =176$$ square feet
Question 5
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The inner radius of a cylindrical wooden furniture is $$8$$ m and its outer radius is $$ 12$$ m. The height of the furniture is $$ 35$$ m. Find its lateral surface area. (Use $$\displaystyle \pi ={ 22 }/{ 7 }$$).

A
$$\displaystyle 880{ \ m }^{ 3 }$$

B
$$\displaystyle 880{\ m }^{ 2 }$$

C
$$\displaystyle 88{ \ m }^{ 2 }$$

D
$$\displaystyle 880{\ mm }^{ 2 }$$

Solution

Given: Inner radius of the cylindrical furniture (r) $$=8$$ m
Outer radius of the cylindrical furniture (R)$$=12$$ m
Height of the furniture (h) $$=35 $$m
$$\therefore$$ Lateral Surface area $$=2\pi(R-r)h$$
$$=2\times \dfrac{22}{7}\times (12-8)\times 35$$
$$=2\times 22\times 4 \times 5$$
$$=880 m^2$$
Question 6
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The circumference of a circle is $$200$$ feet and height is $$12$$ feet. Find its curved surface area of a cylinder.

A
$$\displaystyle 2400{ ft }^{ 2 }$$

B
$$\displaystyle 2100{ ft }^{ 2 }$$

C
$$\displaystyle 2300{ ft }^{ 2 }$$

D
$$\displaystyle 2010{ ft }^{ 2 }$$

Solution

Circumference of cylinder is $$C=2πr$$

It is given that the circumference is $$200$$ feet, therefore,

$$C=2πr\\ \Rightarrow 200=2πr\\ \Rightarrow r=\dfrac { 200 }{ 2π } =\dfrac { 100 }{ π }$$

Now, curved surface area of cylinder is $$A=2πrh$$

Here, the radius is $$\dfrac { 100 }{ π }$$ ft and height is $$12$$ ft.

Thus,

$$A=2πrh=2π\times \dfrac { 100 }{ π } \times 12=2\times 100\times 12=2400$$ ft$$^2$$

Hence, the curved surface area of the cylinder is $$2400$$ ft$$^2$$.
Question 7
1 / -0

If the lateral surface of a cylinder is $$\displaystyle 500\ { cm }^{ 2 }$$ and ts height is $$10\ cm$$, then find radius of its base. (use $$\displaystyle \pi =3.14$$).

A
$$6.92\ cm$$

B
$$7.96\ cm$$

C
$$\displaystyle 6.54\ cm $$

D
$$\displaystyle 8.22\ cm$$

Solution

Here, the lateral surface area is $$A=500\ cm^2$$ and the height is $$h=10\ cm$$
Let, the radius be $$r$$

Lateral surface area of cylinder is $$A=2πrh$$

Thus,
$$A=2πrh\\ \Rightarrow 500=2\times 3.14\times r\times 10\\ \Rightarrow 500=62.8r\\ \Rightarrow r=\dfrac { 500 }{ 62.8 } =7.96$$

Hence, radius of the cylinder is $$7.96\ cm$$ .
Question 8
1 / -0

The curved surface of a cylinder is $$\displaystyle 1000{ \ mm }^{ 2 }$$ and the radius is $$20$$ mm. Find height of the cylinder. (Round off the answer to nearest whole number).

A
$$\displaystyle 8{\ mm }$$

B
$$\displaystyle 9{\ mm }$$

C
$$\displaystyle 7.9{\ mm }$$

D
$$\displaystyle 7.96{\ mm }$$

Solution

Curved surface area of cylinder is $$A=2πrh$$

Here, the curved surface area is $$A=1000$$ mm$$^2$$ the radius is $$r=20$$ mm.

Thus,

$$A=2πrh\\ \Rightarrow 1000=2\times \frac { 22 }{ 7 } \times 20\times h\\ \Rightarrow 1000\times 7=2\times 22\times 20\times h\\ \Rightarrow 7000=880\times h\\ \Rightarrow h=\frac { 7000 }{ 880 } =7.96$$

Hence, height of the cylinder is $$7.96$$ mm.
Question 9
1 / -0

Find the curved surface area of the cylinder given above:

A
$$\displaystyle 1507.2{ m }^{ 2 }$$

B
$$\displaystyle 1527.6{ m }^{ 2 }$$

C
$$\displaystyle 1517.8{ m }^{ 2 }$$

D
$$\displaystyle 1588.1{ m }^{ 3 }$$

Solution

Given,
Height $$h=40\ m$$
Diameter = $$\displaystyle 12m$$

Radius $$r= \dfrac {Diameter}{2} = \dfrac {12}{2}\ m = 6$$ m

Curved surface area $$=\displaystyle 2\pi rh$$
$$\displaystyle =2\times 3.14\times 6\times 40\ m^2$$
$$\displaystyle = 1507.2{ m }^{ 2 }$$

So, option A is correct.
Question 10
1 / -0

The radius of the base of a cylinder is 20 cm and the height is 12 cm. Find the surface area of the cylinder. (Assume $$\displaystyle \pi =3.14$$).

A
$$\displaystyle 4019.2{ cm }^{ 3 }$$

B
$$\displaystyle 4019.2cm$$

C
$$\displaystyle 4019.2{ cm }^{ 2 }$$

D
$$\displaystyle 4018.6{ cm }^{ 2 }$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$

Here, radius is $$r=20$$ cm and the height is $$h=12$$ cm.

Thus,

$$A=2πr(r+h)=2\times 3.14\times 20(20+12)=125.6\times 32=4019.2$$

Hence, the surface area of the cylinder is $$4019.2$$ cm$$^2$$.

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Mensuration Test - 26

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Mensuration Test - 26

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Question 1

$$\displaystyle 1505.1{ in }^{ 2 }$$

$$\displaystyle 1506.5{ in }^{ 2 }$$

$$\displaystyle 1507.5{ in }^{ 2 }$$

$$\displaystyle 1507.2{ in }^{ 2 }$$

Solution

Question 2

$$\displaystyle 0.46\pi $$

$$\displaystyle 0.46\pi { m }^{ 3 }$$

$$\displaystyle 0.46\pi { m }^{ 2 }$$

$$\displaystyle 0.46\pi cm$$

Solution

Question 3

$$\displaystyle 1526.04{\ in }^{ 2 }$$

$$\displaystyle 1525.03{\ in }^{ 2 }$$

$$\displaystyle 1526.04\ in$$

$$\displaystyle 1526.04{\ in }^{ 3 }$$

Solution

Question 4

$$\displaystyle 88{ ft }^{ 2 }$$

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

$$\displaystyle 79{ ft }^{ 2 }$$

$$\displaystyle 176{ ft }^{ 2 }$$

Solution

Question 5

$$\displaystyle 880{ \ m }^{ 3 }$$

$$\displaystyle 880{\ m }^{ 2 }$$

$$\displaystyle 88{ \ m }^{ 2 }$$

$$\displaystyle 880{\ mm }^{ 2 }$$

Solution

Question 6

$$\displaystyle 2400{ ft }^{ 2 }$$

$$\displaystyle 2100{ ft }^{ 2 }$$

$$\displaystyle 2300{ ft }^{ 2 }$$

$$\displaystyle 2010{ ft }^{ 2 }$$

Solution

Question 7

$$6.92\ cm$$

$$7.96\ cm$$

$$\displaystyle 6.54\ cm $$

$$\displaystyle 8.22\ cm$$

Solution

Question 8

$$\displaystyle 8{\ mm }$$

$$\displaystyle 9{\ mm }$$

$$\displaystyle 7.9{\ mm }$$

$$\displaystyle 7.96{\ mm }$$

Solution

Question 9

$$\displaystyle 1507.2{ m }^{ 2 }$$

$$\displaystyle 1527.6{ m }^{ 2 }$$

$$\displaystyle 1517.8{ m }^{ 2 }$$

$$\displaystyle 1588.1{ m }^{ 3 }$$

Solution

Question 10

$$\displaystyle 4019.2{ cm }^{ 3 }$$

$$\displaystyle 4019.2cm$$

$$\displaystyle 4019.2{ cm }^{ 2 }$$

$$\displaystyle 4018.6{ cm }^{ 2 }$$

Solution

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