Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 37

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Weekly Quiz Competition

Question 1
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 2
1 / -0

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 3
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 4
1 / -0

David built a recycling cylindrical bin that is 12 feet long and its base is 56 feet radius. Find the surface area of the bin.

A
$$\displaystyle 23936{\ ft }^{ 3 }$$

B
$$\displaystyle 23936{\ ft }^{ 2 }$$

C
$$\displaystyle 23950{ \ ft }^{ 2 }$$

D
$$\displaystyle 23936\ ft$$

Solution

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

Here the cylindrical bin has radius $$r=56$$ ft and height $$h=12$$ ft.

Thus,

$$A=2πr(r+h)=2\times 3.14\times 56(56+12)=351.68\times 68=23936.24$$

Hence, the surface area of the cylindrical bin is approximately equal to $$23936$$ ft$$^2$$.
Question 5
1 / -0

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 6
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 7
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$$^2$$.
Question 8
1 / -0

Find the height of a cylinder that has a diameter of $$10$$ feet and a surface area of $$\displaystyle 220{\ ft }^{ 2 }$$. Round your answer to the nearest whole number.
(use $$\displaystyle \pi ={ 22 }/{ 7 }$$).

A
$$0.1$$ ft

B
$$3$$ ft

C
$$2$$ ft

D
$$1$$ ft

Solution

Surface area of cylinder is $$A=2πr(r+h)$$
Here the cylinder has surface area $$A=220$$ ft$$^2$$ and diameter $$10$$ ft and therefore, the radius is half of the diameter that is$$r=5$$ ft.
Thus,
$$A=2πr(r+h)\\ \Rightarrow 220=2\times \frac { 22 }{ 7 } \times 5(5+h)\\ \Rightarrow 220=\frac { 44 }{ 7 } (25+5h)\\ \Rightarrow 220\times 7=1100+220h\\ \Rightarrow 1540-1100=220h\\ \Rightarrow 220h=440\\ \Rightarrow h=\frac { 440 }{ 220 } =2$$
Hence, the height of the cylinder is $$2$$ ft.
Question 9
1 / -0

A cylindrical drum has its height 20 inches and curved surface area as $$\displaystyle 200{ in }^{ 2 }$$. Find surface area of cylindrical drum.($$\displaystyle \pi ={ 22 }/{ 7 }$$)

A
$$\displaystyle 203.5{ in }^{ 2 }$$

B
$$\displaystyle 207.3{ in }^{ 2 }$$

C
$$\displaystyle 215.7{ in }^{ 2 }$$

D
$$\displaystyle 218.13$$

Solution
Question 10
1 / -0

Judah wants to make a cylindrical drum that will fit a bass with a height $$15 $$in. and a diameter of $$48$$ in. What is the surface area of the drum?
Take $$\pi = 3.14$$

A
$$\displaystyle 5810.10in$$

B
$$\displaystyle 5810.10{ in }^{ 2 }$$

C
$$\displaystyle 5878.08{ in }^{ 2 }$$

D
$$\displaystyle 5878{ in }^{ 2 }$$

Solution

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

Here, diameter is $$48$$ in and therefore, the radius is half of diameter that is $$r=24$$ in and the height is $$h=15$$ in.

Thus,

$$A=2πr(r+h)=2\times 3.14\times 24(24+15)=150.72\times 39=5878.08$$

Hence, the surface area of the cylindrical drum is $$5878.08$$ in$$^2$$.

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Surface Areas and Volumes Test - 37

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Surface Areas and Volumes Test - 37

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SHARING IS CARING

Question 1

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

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

$$\displaystyle 1526.04\ in$$

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

Solution

Question 2

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

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

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

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

Solution

Question 3

$$6.92\ cm$$

$$7.96\ cm$$

$$\displaystyle 6.54\ cm $$

$$\displaystyle 8.22\ cm$$

Solution

Question 4

$$\displaystyle 23936{\ ft }^{ 3 }$$

$$\displaystyle 23936{\ ft }^{ 2 }$$

$$\displaystyle 23950{ \ ft }^{ 2 }$$

$$\displaystyle 23936\ ft$$

Solution

Question 5

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

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

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

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

Solution

Question 6

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

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

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

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

Solution

Question 7

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

$$\displaystyle 4019.2cm$$

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

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

Solution

Question 8

$$0.1$$ ft

$$3$$ ft

$$2$$ ft

$$1$$ ft

Solution

Question 9

$$\displaystyle 203.5{ in }^{ 2 }$$

$$\displaystyle 207.3{ in }^{ 2 }$$

$$\displaystyle 215.7{ in }^{ 2 }$$

$$\displaystyle 218.13$$

Solution

Question 10

$$\displaystyle 5810.10in$$

$$\displaystyle 5810.10{ in }^{ 2 }$$

$$\displaystyle 5878.08{ in }^{ 2 }$$

$$\displaystyle 5878{ in }^{ 2 }$$

Solution

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