Mensuration Test

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Mensuration Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Find the total surface area of the given cuboid.

A
$$\displaystyle 130{ m }^{ 2 }$$

B
$$\displaystyle 131{ m }^{ 2 }$$

C
$$\displaystyle 132{ m }^{ 2 }$$

D
$$\displaystyle 133{ m }^{ 2 }$$

Solution

Given, length $$(l)=8\ m$$
breadth $$(b)=5\ m$$
height $$(h)=2\ m$$

Surface area of the cuboid $$\displaystyle =2\times \left( lb+lh+bh \right) $$

$$\displaystyle =2\times \left( 8\times 5+8\times 2+5\times 2 \right) \ m^2$$

$$\displaystyle =2\times \left( 40+16+10 \right) \ m^2$$

$$\displaystyle =2\times 66\ m^2$$

$$\displaystyle =132\ { m }^{ 2 }$$

Hence, total surface area is $$132\ { m }^{ 2 }$$
Question 2
1 / -0

The edge of the cube measures $$9$$ cm. Find its surface area.

A
$$\displaystyle 418{ cm }^{ 2 }$$

B
$$\displaystyle 446{ cm }^{ 2 }$$

C
$$\displaystyle 486{ cm }^{ 2 }$$

D
$$\displaystyle 441{ cm }^{ 2 }$$

Solution

Given, edge $$= 9 \text{ cm}$$
Total surface area of a cube $$=6\times \text{side}^2$$
$$= 6\times 9\times 9$$
$$= 486 \text{ cm}^2$$
Question 3
1 / -0

Kyle bought 2 snack boxes. Box A has a measure of $$2\ in\times 3\ in\times 5 \ in.$$ Box B has a measure of $$11 \ in\times 4\ in \times 3\ in.$$ Find the surface area of the boxes and their difference.

A
$$\displaystyle 116{ in }^{ 2 }$$

B
$$\displaystyle 201{ in }^{ 2 }$$

C
$$\displaystyle 279{ in }^{ 2 }$$

D
$$\displaystyle 198{in }^{ 2 }$$

Solution

Surface area of rectangle is 2 x (Length x width + Length x height + Width x height)

Here Box A has length $$= 2$$ in, height $$= 3$$ in and width $$= 5$$ in

Therefore, the surface area of Box A is:

$$A=2((2\times 5)+(2\times 3)+(3\times 5))=2(10+6+15)=2\times 31=62$$ in$$^2$$

Now, Box B has length $$= 11$$ in, height $$= 4$$ in and width $$= 3$$ in

Therefore, the surface area of Box B is:

$$A=2((11\times 4)+(11\times 3)+(4\times 3))=2(44+33+12)=2\times 89=178$$ in$$^2$$

Hence, the difference between the surface area of box A and box B is $$178-62=116$$ in$$^2$$.
Question 4
1 / -0

Find the surface area of the cuboid:

A
$$\displaystyle 300.1{ mm }^{ 2 }$$

B
$$\displaystyle 320.5{ mm }^{ 2 }$$

C
$$\displaystyle 316.4{ mm }^{ 2 }$$

D
$$\displaystyle 305.2{ mm }^{ 2 }$$

Solution

Surface area of the cuboid $$=$$ $$\displaystyle 2\times \left( lw+lh+hw \right) $$
$$\displaystyle =2\times \left( 8\times 2.1+8\times 14+2.1\times 14 \right) $$
$$\displaystyle =2\times \left( 16.8+112+29.4 \right) $$
$$\displaystyle =2\times 158.2$$
$$\displaystyle =316.4$$ $${ mm }^{ 2 }$$
Question 5
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 6
1 / -0

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 7
1 / -0

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 8
1 / -0

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 9
1 / -0

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 10
1 / -0

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$$^2$$.

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Mensuration Test - 25

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Mensuration Test - 25

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SHARING IS CARING

Question 1

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

$$\displaystyle 131{ m }^{ 2 }$$

$$\displaystyle 132{ m }^{ 2 }$$

$$\displaystyle 133{ m }^{ 2 }$$

Solution

Question 2

$$\displaystyle 418{ cm }^{ 2 }$$

$$\displaystyle 446{ cm }^{ 2 }$$

$$\displaystyle 486{ cm }^{ 2 }$$

$$\displaystyle 441{ cm }^{ 2 }$$

Solution

Question 3

$$\displaystyle 116{ in }^{ 2 }$$

$$\displaystyle 201{ in }^{ 2 }$$

$$\displaystyle 279{ in }^{ 2 }$$

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

Solution

Question 4

$$\displaystyle 300.1{ mm }^{ 2 }$$

$$\displaystyle 320.5{ mm }^{ 2 }$$

$$\displaystyle 316.4{ mm }^{ 2 }$$

$$\displaystyle 305.2{ mm }^{ 2 }$$

Solution

Question 5

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

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

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

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

Solution

Question 6

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

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

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

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

Solution

Question 7

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

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

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

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

Solution

Question 8

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

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

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

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

Solution

Question 9

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

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

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

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

Solution

Question 10

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

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

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

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

Solution

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