Surface Areas and Volumes Test

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Surface Areas and Volumes Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

Calculate the total surface area of the cuboid:

A
$$\displaystyle 171\ { cm }^{ 2 }$$

B
$$\displaystyle 172\ { cm }^{ 2 }$$

C
$$\displaystyle 173\ { cm }^{ 2 }$$

D
$$\displaystyle 174\ { cm }^{ 2 }$$

Solution

Total surface area of the cuboid $$\displaystyle 2\times \left( lw+lh+hw \right) $$
$$\displaystyle =2\times \left( 10\times 1+10\times 7+7\times 1 \right) $$
$$\displaystyle =2\times \left( 10+70+7 \right) $$
$$\displaystyle =2\times 87$$
$$=\displaystyle 174{ cm }^{ 2 }$$

So, option D is correct.
Question 2
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The side of the base of a dice is $$5.5$$ mm. Find the surface area of a dice whose edges are squares.

A
$$\displaystyle 181.5{ mm }^{ 2 }$$

B
$$\displaystyle 90.21{ mm }^{ 2 }$$

C
$$\displaystyle 180.2{ mm }^{ 2 }$$

D
$$\displaystyle 120.4{ mm }^{ 2 }$$

Solution

Given, side of base $$=5.5$$ mm
Total surface area of a cube $$=$$ $$\displaystyle 6\times $$ side$$^{ 2 }$$
$$\displaystyle =6\times 5.5\times 5.5$$
$$\displaystyle =181.5{ mm }^{ 2 }$$
Question 3
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Find the surface area of a cube with side $$\displaystyle 12$$ m

A
$$\displaystyle 814{ m }^{ 2 }$$

B
$$\displaystyle 864{ m }^{ 2 }$$

C
$$\displaystyle 854{ m }^{ 2 }$$

D
$$\displaystyle 841{ m }^{ 2 }$$

Solution

Total surface area of a cube $$=$$ $$\displaystyle 6\times $$ side$$^{ 2 }$$
$$\displaystyle =6\times 12\times 12$$
$$\displaystyle =864{ m }^{ 2 }$$
Question 4
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A cubical water tank measures $$3$$ feet sides. Find its surface area.

A
$$\displaystyle 9{ ft }^{ 2 }$$

B
$$\displaystyle 50{ ft }^{ 2 }$$

C
$$\displaystyle 52{ ft }^{ 2 }$$

D
$$\displaystyle 54{ ft }^{ 2 }$$

Solution

$$Surface\ area\ of\ a\ cube=6\times Side^2$$
$$side=3ft$$
$$Surface\ Area=6\times 3^2$$
$$Surface\ Area=6\times 9$$
$$Surface\ Area=54ft^2$$
Question 5
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The length of the side is $$3.9$$ ft. Find the surface area of a cube .

A
$$\displaystyle 41.82{ ft }^{ 2 }$$

B
$$\displaystyle 94.16{ ft }^{ 2 }$$

C
$$\displaystyle 91.26{ ft }^{ 2 }$$

D
$$\displaystyle 40.41{ ft }^{ 2 }$$

Solution

Given, length of side $$=.9$$ ft
Total surface area of a cube $$=$$ $$\displaystyle 6\times $$ side$$^{ 2 }$$
$$\displaystyle =6\times 3.9\times 3.9$$
$$\displaystyle =91.26{ ft }^{ 2 }$$
Question 6
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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 7
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The diameter of a cylinder is $$12$$ m and its height is $$10$$ m. Find the curved surface area of a cylinder.

A
$$\displaystyle 240\pi { cm }^{ 2 }$$

B
$$\displaystyle 120\pi { m }^{ 2 }$$

C
$$\displaystyle 220\pi { m }^{ 2 }$$

D
$$\displaystyle 230\pi { mm }^{ 2 }$$

Solution

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

Here, the diameter is $$12$$ m and therefore, the radius is half of diameter that is $$r=6$$ m and height is $$10$$ m.

Thus,

$$A=2πrh=2\times π\times 6\times 10=120π$$ m$$^2$$

Hence, the curved surface area of the cylinder is $$120π$$ m$$^2$$.
Question 8
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Choose the correct formula for surface area of a cylinder.

A
$$\displaystyle 2\pi { r }^{ 2 }+2\pi rh$$

B
$$\displaystyle \pi { r }^{ 2 }+\pi rh$$

C
$$\displaystyle 2\pi r+2\pi rh$$

D
$$\displaystyle 2\pi { r }^{ 2 }+\pi rh$$

Solution

A cylinder comprises two circles and one rectangle as given in the figure
The surface area of a circle is $$\pi r^2$$ where $$r$$ is the radius and the surface area of a rectangle is $$2\pi rh$$.
$$\implies$$ Surface area of cylinder $$=2\times$$ area of the circular base $$+$$ area of the rectangle
$$\Rightarrow $$ Surface area of cylinder $$=2\pi r^2+2\pi rh$$
Question 9
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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 10
1 / -0

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.

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Surface Areas and Volumes Test - 36

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Surface Areas and Volumes Test - 36

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Question 1

$$\displaystyle 171\ { cm }^{ 2 }$$

$$\displaystyle 172\ { cm }^{ 2 }$$

$$\displaystyle 173\ { cm }^{ 2 }$$

$$\displaystyle 174\ { cm }^{ 2 }$$

Solution

Question 2

$$\displaystyle 181.5{ mm }^{ 2 }$$

$$\displaystyle 90.21{ mm }^{ 2 }$$

$$\displaystyle 180.2{ mm }^{ 2 }$$

$$\displaystyle 120.4{ mm }^{ 2 }$$

Solution

Question 3

$$\displaystyle 814{ m }^{ 2 }$$

$$\displaystyle 864{ m }^{ 2 }$$

$$\displaystyle 854{ m }^{ 2 }$$

$$\displaystyle 841{ m }^{ 2 }$$

Solution

Question 4

$$\displaystyle 9{ ft }^{ 2 }$$

$$\displaystyle 50{ ft }^{ 2 }$$

$$\displaystyle 52{ ft }^{ 2 }$$

$$\displaystyle 54{ ft }^{ 2 }$$

Solution

Question 5

$$\displaystyle 41.82{ ft }^{ 2 }$$

$$\displaystyle 94.16{ ft }^{ 2 }$$

$$\displaystyle 91.26{ ft }^{ 2 }$$

$$\displaystyle 40.41{ ft }^{ 2 }$$

Solution

Question 6

$$\displaystyle 8{\ mm }$$

$$\displaystyle 9{\ mm }$$

$$\displaystyle 7.9{\ mm }$$

$$\displaystyle 7.96{\ mm }$$

Solution

Question 7

$$\displaystyle 240\pi { cm }^{ 2 }$$

$$\displaystyle 120\pi { m }^{ 2 }$$

$$\displaystyle 220\pi { m }^{ 2 }$$

$$\displaystyle 230\pi { mm }^{ 2 }$$

Solution

Question 8

$$\displaystyle 2\pi { r }^{ 2 }+2\pi rh$$

$$\displaystyle \pi { r }^{ 2 }+\pi rh$$

$$\displaystyle 2\pi r+2\pi rh$$

$$\displaystyle 2\pi { r }^{ 2 }+\pi rh$$

Solution

Question 9

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

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

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

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

Solution

Question 10

$$\displaystyle 0.46\pi $$

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

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

$$\displaystyle 0.46\pi cm$$

Solution

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