2 Mark Question - Maths STD 8 Questions - Vidyadip

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2 Mark Question

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16 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks

Find the volume of the cylinder if the circumference of the base of cylinder is 132 cm and height is 25 cm.

Answer

Given: Circumference of the base of cylinder $=132 cm$ and height $(h)=25 cm$
To find: Volume of the cylinder
i. Circumference of base of cylinder $=2 \pi r$
$
\begin{aligned}
& \therefore 132=2 \times \frac{22}{7} \times r \\
& \therefore \frac{132 \times 7}{2 \times 22}=r \\
& \therefore \frac{6 \times 7}{2}=r \\
& \therefore 3 \times 7=r \\
& \therefore r=21 cm
\end{aligned}
$

ii. Volume of the cylinder $=\pi r^2 h$
$
\begin{aligned}
& =\frac{22}{7} \times 21 \times 21 \times 25 \\
& =22 \times 3 \times 21 \times 25 \\
& =34650 cc
\end{aligned}
$
$\therefore$ The volume of the cylinder is $34650 cc$.

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Question 22 Marks

How much water will a tank hold if the interior diameter of the tank is 1.6 m and its depth is 0.7 m ?

Answer

Given: interior diameter of the tank (d) $=1.6 m$ and depth $( h )=0.7 m$
To find: Capacity of the tank
interior diameter of the tank $( d )=1.6 m$
$\therefore$ Interior radius $(r)=\frac{ d }{2}=\frac{1.6}{2}$
$=0.8 m$
$=0.8 \times 100$
$\ldots[\because 1 m =100 cm ]$
$=80 cm$
$h =0.7 m =0.7 \times 100=70 cm$
Capacity of the tank $=$ Volume of the tank $=\pi r^2 h$ $=\frac{22}{7} \times 80 \times 80 \times 70$
$=22 \times 80 \times 80 \times 10$
$=1408000 cc$
$=\frac{1408000}{1000}$
$\ldots[\because 1$ litre $=1000 cc ]$
$=1408$ litre
$\therefore$ The tank can hold 1408 litre of water.

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Question 32 Marks

How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm ?

Answer

Given: For cylindrical rod: length of rod $(h)=90 cm$, and diameter $( d )=1.4 cm$
To find: Iron required to make a rod
$\operatorname{diameter}( d )=1.4 cm$
$\therefore$ radius $(r)=\frac{ d }{2}=\frac{1.4}{2}=0.7 cm$
Volume of rod $=\pi r^2 h$
$=\frac{22}{7} \times 0.7 \times 0.7 \times 90$
$=22 \times 0.1 \times 0.7 \times 90$
$=138.60 cc$
$\therefore 138.60 cc$ of iron is required to make the rod.

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Question 42 Marks

Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.

r = 5.6 cm, h = 5 cm

Answer

Given: $r=5.6 cm$ and $h =5 cm$
To find: Volume of the cylinder
Volume of the cylinder $=\pi r^2 h$
$
\begin{aligned}
& =\frac{22}{7} \times 5.6 \times 5.6 \times 57 \\
& =22 \times 0.8 \times 5.6 \times 5 \\
& =492.8 cc
\end{aligned}
$
$\therefore$ The volume of the cylinder is $492.8 cc$.

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Question 52 Marks

Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.

r = 4.2 cm, h = 5 cm

Answer

Given: $r=4.2 cm$ and $h =5 cm$
To find: Volume of the cylinder
Volume of the cylinder $=\pi r^2 h$
$
\begin{aligned}
& =\frac{22}{7} \times 4.2 \times 4.2 \times 5 \\
& =22 \times 0.6 \times 4.2 \times 5 \\
& =277.2 cc
\end{aligned}
$
$\therefore$ The volume of the cylinder is $277.2 cc$.

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Question 62 Marks

Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.

r = 2.5 m, h = 7 m

Answer

Given: $r=2.5 m$ and $h =7 m$
To find: Volume of the cylinder
Volume of the cylinder $=\pi r^2 h$
$=\frac{22}{7} \times 2.5 \times 2.5 \times 7$
$=22 \times 2.5 \times 2.5$
$=137.5$ cu.m
$\therefore$ The volume of the cylinder is 137.5 cu.m.

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Question 72 Marks

Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.

r = 10.5 cm, h = 8 cm

Answer

Given: $r=10.5 cm$ and $h =8 cm$
To find: Volume of the cylinder
Volume of the cylinder $=\pi r^2 h$
$=\frac{22}{7} \times 10.5 \times 10.5 \times 8$
$=22 \times 1.5 \times 10.5 \times 8$
$=2772 cc$
$\therefore$ The volume of the cylinder is $2772 cc$.

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Question 82 Marks

Find the area of base and radius of a cylinder if its curved surface area is 660 sq.cm and height is 21 cm.
Given: Curved surface area = 660 sq.cm, and height = 21 cm
To find: area of base and radius of a cylinder

Answer

$
\begin{aligned}
& \text { i. Curved surface area of cylinder }=2 \pi r h \\
& \therefore 660=2 \times \frac{22}{7} \times r \times 21 \\
& \therefore 660=2 \times 22 \times r \times 3 \\
& \therefore \frac{660}{2 \times 22 \times 3}=r \\
& \therefore \frac{660}{2 \times 66}=r \\
& \therefore 5=r \\
& \text { i.e., } r=5 cm
\end{aligned}
$

ii. Area of a base of the cylinder $=\pi r^2$
$
\begin{aligned}
& =\frac{22}{7} \times 5 \times 5 \\
& =\frac{550}{7} \\
& =78.57 \text { sq. } cm
\end{aligned}
$
$\therefore$ The radius of the cylinder is $5 cm$ and the area of its base is 78.57 sq.cm.

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Question 92 Marks

Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and height is 45 cm. (π = 3.14)
Given: For cylindrical drum:
Diameter (d) = 50 cm
and height (h) = 45 cm
To find: Total surface area of the cylindrical drum

Answer

$
\begin{aligned}
& \text { Diameter }(d)=50 cm \\
& \therefore \text { radius }(r)=\frac{d}{2}=\frac{50}{2}=25 cm
\end{aligned}
$
Total surface area of the cylindrical drum $=2 \pi r(h+r)$
$
\begin{aligned}
& =2 \times 3.14 \times 25(45+25) \\
& =2 \times 3.14 \times 25 \times 70 \\
& =10,990 \text { sq.cm }
\end{aligned}
$
$\therefore$ The total surface area of the cylindrical drum is 10,990 sq.cm.

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Question 102 Marks

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.

r = 4.2 cm, h = 14 cm

Answer

Given: $r=4.2 cm$ and $h =14 cm$
To find: Curved surface area of cylinder and total surface area Curved surface area of the cylinder $=2 \pi rh$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 4.2 \times 14=2 \times 22 \times 4.2 \times 2 \\
& =369.60 \text { sq }. cm
\end{aligned}
$
Total surface area of the cylinder $=2 \pi r(h+r)$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 4.2(14+4.2) \\
& =2 \times \frac{22}{7} \times 4.2 \times 18.2 \\
& =2 \times 22 \times 0.6 \times 18.2 \\
& =480.48 \text { sq.cm }
\end{aligned}
$
$\therefore$ The curved surface area of the cylinder is 369.60 sq.cm and its total surface area is $480.48 sq . cm$.

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Question 112 Marks

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.

r = 70 cm, h = 1.4 cm

Answer

Given: $r=70 cm$ and $h =1.4 cm$
To find: Curved surface area of cylinder and total surface area Curved surface area of the cylinder $=2 \pi r h$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 70 \times 1.4 \\
& =2 \times 22 \times 10 \times 1.4 \\
& =616 \text { sq.cm }
\end{aligned}
$
Total surface area of the cylinder $=2 \pi r(h+r)$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 70(1.4+70) \\
& =2 \times \frac{22}{7} \times 70 \times 71.4 \\
& =2 \times 22 \times 10 \times 71.4 \\
& =2 \times 22 \times 714 \\
& =31416 \text { sq.cm }
\end{aligned}
$
$\therefore$ The curved surface area of the cylinder is 616 sq.cm and its total surface area is 31416 sq.cm.

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Question 122 Marks

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.

r = 2.5 cm, h = 7 cm

Answer

Given: $r =2.5 cm$ and $h =7 cm$
To find: Curved surface area of cylinder and total surface area Curved surface area of the cylinder $=2 \pi r h$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 2.5 \times 7 \\
& =2 \times 22 \times 2.5 \\
& =110 \text { sq.cm }
\end{aligned}
$
Total surface area of the cylinder $=2 \pi r(h+r)$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 2.5(7+2.5) \\
& =2 \times \frac{22}{7} \times 2.5 \times 9.5 \\
& =\frac{1045}{7} \\
& =149.29 \text { sq.cm }
\end{aligned}
$
$\therefore$ The curved surface area of the cylinder is 110 sq.cm and its total surface area is 149.29 sq.cm.

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Question 132 Marks

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.

r = 1.4 cm, h = 2.1 cm

Answer

Given: $r=1.4 cm$ and $h=2.1 cm$
To find: Curved surface area of cylinder and total surface area
Curved surface area of the cylinder $=2 \pi r h$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 1.4 \times 2.1 \\
& =2 \times 22 \times 0.2 \times 2.1 \\
& =18.48 \text { sq.cm }
\end{aligned}
$
Total surface area of the cylinder $=2 \pi r(h+r)$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 1.4(2.1+1.4) \\
& =2 \times \frac{22}{7} \times 1.4 \times 3.5 \\
& =2 \times 22 \times 0.2 \times 3.5 \\
& =30.80 \text { sq.cm }
\end{aligned}
$
$\therefore$ The curved surface area of the cylinder is 18.48 sq.cm and its total surface area is 30.80 sq.cm.

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Question 142 Marks

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.

r = 7 cm, h = 10 cm

Answer

Given: $r=7 cm$ and $h =10 cm$
To find: Curved surface area of cylinder and total surface area Curved surface area of the cylinder $=2 \pi r h$
$
\begin{aligned}
& =2 \times \frac{22}{7} \times 7 \times 10 \\
& =2 \times 22 \times 10 \\
& =440 \text { sq.cm }
\end{aligned}
$
Total surface area of the cylinder:
$
\begin{aligned}
& =2 \pi r(h+r) \\
& =2 \times \frac{22}{7} \times 7(10+7) \\
& =2 \times \frac{22}{7} \times 7 \times 17 \\
& =2 \times 22 \times 17 \\
& =748 \text { sq.cm }
\end{aligned}
$
The curved surface area of the cylinder is 440 sq.cm and its total surface area is 748 sq.cm.

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Question 152 Marks

A cuboid shaped soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm.
Given: For cuboid shaped soap bar,
length (l) = 10 cm, breadth (b) = 5 cm and volume = 150 cc
To find: Thickness of the soap bar (h)

Answer

Volume of soap bar $=1 \times b \times h$
$
\begin{aligned}
& \therefore 150=10 \times 5 \times h \\
& \therefore 150=50 h \\
& \therefore \frac{150}{50}=h \\
& \therefore 3= h
\end{aligned}
$
i.e., $h=3 cm$
$\therefore$ The thickness of the soap bar is $3 cm$.

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Question 162 Marks

Find the volume of a box if its length, breadth and height are 20 cm, 10.5 cm and 8 cm respectively.
Given: For cuboid shaped box,
length (l) = 20 cm, breadth (b) = 10.5 cm and height (h) = 8cm
To find: Volume of a box

Answer

Volume of a box = l x b x h
= 20 x 10.5 x 8
= 1680 cc
∴ The volume of the box is 1680 cc.

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