Surface Areas and Volumes Test

Result

Surface Areas and Volumes Test - 38

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Edward bought a container of ceralac in the shape of cylinder. If the container has a radius $$10 m$$ and a surface area is $$\displaystyle 340\pi $$. What is its height?

A
$$5 m$$

B
$$6m$$

C
$$7m$$

D
$$8m$$

Solution

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

Here the cylindrical container has surface area $$A=340π$$ m$$^2$$ and radius $$r=10$$ m.

Thus,

$$A=2πr(r+h)\\ \Rightarrow 340π=2π\times 10(10+h)\\ \Rightarrow 340π=20π(10+h)\\ \Rightarrow 340π=200π+20πh\\ \Rightarrow 20πh=340π-200π\\ \Rightarrow 20πh=140π\\ \Rightarrow h=\dfrac { 140π }{ 20π } =7$$

Hence, the height of the cylindrical container is $$7m$$.
Question 2
1 / -0

The surface area of a cylindrical box is $$\displaystyle 132\ { mm }^{ 2 }$$ and its height is $$4 \ mm.$$ Find its radius.

A
$$\displaystyle 2 $$ $${ mm }$$

B
$$\displaystyle 3 $$ $${ mm }$$

C
$$\displaystyle 4 $$ $${ mm }$$

D
$$\displaystyle 5 $$ $${ mm }$$

Solution

Given: Cylindrical box has surface area $$A=132$$ $$mm^2$$ and height $$h=4\ mm$$

We know surface area of cylinder is $$A=2πr(r+h)$$

Thus, $$ 132=2\times \dfrac { 22 }{ 7 } \times r(r+4)$$

$$ \Rightarrow 132=\dfrac { 44 }{ 7 } r(r+4)$$

$$ \Rightarrow 132\times 7=44r(r+4)$$

$$\Rightarrow 924=44r^{ 2 }+176r$$

$$\Rightarrow 44r^{ 2 }+176r-924=0$$

$$ \Rightarrow r^{ 2 }+4r-21=0$$

$$ \Rightarrow r^{ 2 }+7r-3r-21=0$$

$$ \Rightarrow r(r+7)-3(r+7)=0$$

$$ \Rightarrow r+7=0,\quad r-3=0$$

$$ \Rightarrow r=-7,\quad r=3$$

Hence, the radius of the cylindrical box is $$3$$ mm.
Question 3
1 / -0

A skating board rocks back and forth on a wooden cylinder. The cylinder has a radius of 6 inches and a surface area is $$\displaystyle 590{ in }^{ 2 }$$. Find the height of the cylinder. ($$\displaystyle \pi =3.14$$).

A
$$10$$ in

B
$$9.65$$ in

C
$$9$$ in

D
$$9.5$$ in

Solution

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

Here the wooden cylinder has surface area $$A=590$$ in$$^2$$ and radius $$r=6$$ mm.

Thus,

$$A=2πr(r+h)\\ \Rightarrow 590=2\times \dfrac { 22 }{ 7 } \times 6(6+h)\\ \Rightarrow 590=\dfrac { 44 }{ 7 } (36+6h)\\ \Rightarrow 590\times 7=1584+264h\\ \Rightarrow 4130-1584=264h\\ \Rightarrow 264h=2546\\ \Rightarrow h=\dfrac { 2546 }{ 264 } =9.643$$

Hence, the height of the wooden cylinder is $$9.65$$ in.
Question 4
1 / -0

Find the surface area of a cylinder with the following dimension:
Height $$= 10$$ ft.
Radius $$= 2$$ ft.

A
$$\displaystyle 82\pi { ft }^{ 2 }$$

B
$$\displaystyle 78\pi { ft }^{ 2 }$$

C
$$\displaystyle 48\pi { ft }^{ 2 }$$

D
$$\displaystyle 81\pi { ft }^{ 2 }$$

Solution

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

Here, radius is $$r=2$$ ft and the height is $$h=10$$ ft.

Thus,

$$A=2π\times 2(2+10)=2π\times 2\times 12=48π$$

Hence, the surface area of the cylinder is $$48π$$ ft$$^2$$.
Question 5
1 / -0

Find the total surface area of the cylinder. (Use $$\displaystyle \pi =3.14$$).

A
$$\displaystyle 678.99{ ft }^{ 2 }$$

B
$$\displaystyle 3881.05{ ft }^{ 2 }$$

C
$$\displaystyle 3881.04ft$$

D
$$\displaystyle 678.24{ ft }^{ 2 }$$

Solution

Given: $$r=6ft$$ and $$h=12ft$$
The total surface area of a cylinder = $$\displaystyle 2\pi r\left( r+h \right) $$
$$\displaystyle =2\times 3.14\times 6\left( 6+12 \right) $$
$$\displaystyle =2\times 3.14\times 6\left( 18 \right) $$
$$=\displaystyle 678.24{ ft }^{ 2 }$$

So, option D is correct.
Question 6
1 / -0

A gas cylinder has a diameter of $$14 $$m and height is $$0.2$$m. Find its surface area. ($$\displaystyle \pi ={ 22 }/{ 7 }$$)

A
$$\displaystyle 316.512{ mm }^{ 2 }$$

B
$$\displaystyle 316.512m$$

C
$$\displaystyle 316.512{ m }^{ 3 }$$

D
$$\displaystyle 316.512{ m }^{ 2 }$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$
Here the gas cylinder has diameter $$14$$ m and therefore, the radius is half of diameter that is $$r=7$$ m and height $$h=0.2$$ m.
Thus,
$$A=2πr(r+h)=2 \times \dfrac {22}{7}\times 7(7+0.2)=316.512$$
Hence, the surface area of the gas cylinder is $$316.512m^2$$.
Question 7
1 / -0

The curved surface area of a cylinder is $$\displaystyle 188.4\ { m }^{ 2 }$$. The height is $$12\ m$$. What is the radius? (use$$\displaystyle \pi =3.14$$).

A
$$\displaystyle 2\ { cm }$$

B
$$\displaystyle 2.5\ cm$$

C
$$\displaystyle 2\ m$$

D
$$\displaystyle 2.5\ m$$

Solution

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

Here, the curved surface area is $$A=188.4\ m^2$$ the height is $$h=12\ m$$.

Thus,

$$A=2πrh\\ \Rightarrow 188.4=2\times 3.14\times r\times 12\\ \Rightarrow 188.4=75.36r\\ \Rightarrow r=\dfrac { 188.4 }{ 75.36 } =2.5$$

Hence, radius of the cylinder is $$2.5\ m$$
Question 8
1 / -0

Find the volume of a sphere whose diameter is $$7.2\ mm$$.

A
$$\displaystyle 195.33{ \ m }^{ 3 }$$

B
$$\displaystyle 175.33{ \ mm }^{ 3 }$$

C
$$\displaystyle 195.33{ \ mm }^{ 3 }$$

D
$$\displaystyle 185.33{\ mm }^{ 3 }$$

Solution

Formula:
Volume of sphere $$=\dfrac{4}{3} \pi r^3$$
$$r=radius$$
Given:
$$diameter(d)=7.2\ mm$$

$$radius(r)=\dfrac{d}{2}=\dfrac{7.2}{2}=3.6\ mm$$

$$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}\times 3.14\times (3.6)^3$$

$$=\dfrac{4}{3}\times 3.6\times 3.6\times 3.6\times 3.14$$

$$=\dfrac{4}{3}\times 46.656times 3.14$$

$$=\dfrac{585.999}{3}$$

$$=195.33\ mm^3$$
Question 9
1 / -0

What is the volume of a sphere? (use $$\displaystyle \pi =3.14$$)

A
$$\displaystyle 6,878.82{\ in }^{ 3 }$$

B
$$\displaystyle 6,578.82{ \ in }^{ 3 }$$

C
$$\displaystyle 5,878.82{\ in }^{ 3 }$$

D
$$\displaystyle 6,808.82{\ in }^{ 3 }$$

Solution

Formula:
Volume of sphere$$=\dfrac{4}{3}\pi r^3$$
where,
$$r=radius$$
Given:
$$r=11.8$$
After substituting the values in the formula we
$$ \dfrac{4}{3}\pi r^3 =\dfrac{4}{3}\times 3.14\times 11.8^3$$
$$=\dfrac{4}{3}\times3.14\times11.8\times11.8\times11.8$$

$$=\dfrac{20636.481}{3}$$
$$=6878.82\ in^3$$
Question 10
1 / -0

The volume of a sphere is $$\displaystyle 1150.35{ in }^{ 3 }$$. Find its radius. (Round off your answer to the nearest whole number).

A
$$2$$ in

B
$$5$$ in

C
$$8$$ in

D
$$7$$ in

Solution

Formula:
Volume of sphere$$=\dfrac{4}{3}\pi r^3$$
where,
$$r=radius$$
Given:
$$volume=1150.35\ in^3$$
After substituting the values in the formula we get:
$$1150.35= \dfrac{4}{3}\pi r^3$$

$$\Rightarrow 1150.35= \dfrac{4}{3}*3.14* r^3$$

$$\Rightarrow \dfrac{1150.35*3}{4*3.14}=r^3$$

$$\Rightarrow r^3=\dfrac{3451.05}{12.56}$$
$$\Rightarrow r^3=274.76$$
$$\Rightarrow r=\sqrt[3]{274.76}$$
$$\Rightarrow r=6.50\approx 7\ in$$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Surface Areas and Volumes Test - 38

Result

Surface Areas and Volumes Test - 38

Score

-

Rank

-

SHARING IS CARING

Question 1

$$5 m$$

$$6m$$

$$7m$$

$$8m$$

Solution

Question 2

$$\displaystyle 2 $$ $${ mm }$$

$$\displaystyle 3 $$ $${ mm }$$

$$\displaystyle 4 $$ $${ mm }$$

$$\displaystyle 5 $$ $${ mm }$$

Solution

Question 3

$$10$$ in

$$9.65$$ in

$$9$$ in

$$9.5$$ in

Solution

Question 4

$$\displaystyle 82\pi { ft }^{ 2 }$$

$$\displaystyle 78\pi { ft }^{ 2 }$$

$$\displaystyle 48\pi { ft }^{ 2 }$$

$$\displaystyle 81\pi { ft }^{ 2 }$$

Solution

Question 5

$$\displaystyle 678.99{ ft }^{ 2 }$$

$$\displaystyle 3881.05{ ft }^{ 2 }$$

$$\displaystyle 3881.04ft$$

$$\displaystyle 678.24{ ft }^{ 2 }$$

Solution

Question 6

$$\displaystyle 316.512{ mm }^{ 2 }$$

$$\displaystyle 316.512m$$

$$\displaystyle 316.512{ m }^{ 3 }$$

$$\displaystyle 316.512{ m }^{ 2 }$$

Solution

Question 7

$$\displaystyle 2\ { cm }$$

$$\displaystyle 2.5\ cm$$

$$\displaystyle 2\ m$$

$$\displaystyle 2.5\ m$$

Solution

Question 8

$$\displaystyle 195.33{ \ m }^{ 3 }$$

$$\displaystyle 175.33{ \ mm }^{ 3 }$$

$$\displaystyle 195.33{ \ mm }^{ 3 }$$

$$\displaystyle 185.33{\ mm }^{ 3 }$$

Solution

Question 9

$$\displaystyle 6,878.82{\ in }^{ 3 }$$

$$\displaystyle 6,578.82{ \ in }^{ 3 }$$

$$\displaystyle 5,878.82{\ in }^{ 3 }$$

$$\displaystyle 6,808.82{\ in }^{ 3 }$$

Solution

Question 10

$$2$$ in

$$5$$ in

$$8$$ in

$$7$$ in

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.