4 Mark Question

Question 14 Marks

Draw a circle of radius 28mm. Draw any one triangle and draw a trapezium on the graph paper. Find the area of these figures by counting the number of small squares on the graph paper. Verify your answers using formula for area of these figures.Observe that smaller the squares of graph paper, better is the approximation of area.

Answer

SELF

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Question 24 Marks

Find the area of the circle if its circumference is 88 cm.

Answer

Circumference of the circle $=88 cm$...[Given]
Circumference of the circle $=2 \pi r$
$\therefore 88=2 \times \frac{22}{7} \times r$
$\therefore r=\frac{88 \times 7}{2 \times 22} \therefore r=14 cm$
Area of the circle $=\pi r^2=\frac{22}{7} \times(14)^2$
$=\frac{22}{7} \times 14 \times 14=22 \times 2 \times 14=616$ sq. $cm$
$\therefore$ The area of circle is $616 Sq.cm$

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Question 34 Marks

Areas of some circles are given below, find their diameters.

12474 sq. cm

Answer

Area of the circle $=12474$ sq. cm ...[Given]
Area of the circle $=\pi r^2$
$
\begin{aligned}
& \therefore 12474=\frac{22}{7} \times r^2 \\
& \therefore r^2=12474 \times \frac{7}{22} \\
& \therefore r^2=567 \times 7 \\
& \therefore r^2=3969 \\
& \therefore r=63 \ldots[\text { Taking square root of both sides] } \\
& \therefore \text { Diameter }=2 r=2 \times 63=126 cm
\end{aligned}
$

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Question 44 Marks

Areas of some circles are given below, find their diameters.

394.24 sq. cm

Answer

Area of the circle $=394.24$ sq. cm ... [Given]
Area of the circle $=\pi r^2$
$\therefore \quad 394.24=\frac{22}{7} \times r ^2$
$\therefore \quad \dot{r}^2=394.24 \times \frac{7}{22}$
$\therefore \quad r^2=\frac{394.24 \times 100}{1 \times 100} \times \frac{7}{22}$
$\therefore \quad r^2=\frac{39424}{100} \times \frac{7}{22}$
$\therefore \quad r^2=\frac{1792}{100} \times 7$
$\therefore \quad r^2=\frac{12544}{100}$
$\therefore \quad r^2=\frac{112^2}{10^2}$
$\therefore \quad r=\frac{112}{10}$
...[Taking square root of both sides]
$\therefore \quad r =11.2 cm$
$\therefore$ Diameter $=2 r=2 \times 11.2=22.4 cm$

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Question 54 Marks

Areas of some circles are given below, find their diameters.

176 sq.cm

Answer

Area of the circle $=176$ sq. cm ... [Given]
Area of the circle $=\pi r^2$
$
\begin{aligned}
& \therefore 176=\frac{22}{7} \times r^2 \\
& \therefore r^2=176 \times \frac{7}{22} \\
& \therefore r^2=56
\end{aligned}
$
$\therefore r =\sqrt{ } 56 \ldots$ [Taking square root of both sides]
Diameter $=2 r=2 \sqrt{ } 56 CM$

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Question 64 Marks

Radii of the circles are given below, find their areas.

17.5 cm

Answer

Radius of the circle $(r)=17.5 cm$... [Given]
Area of the circle $=\pi r^2$
$
\begin{aligned}
& =\frac{22}{7} \times(17.5)^2 \\
& =\frac{22}{7} \times 17.5 \times 17.5 \\
& =22 \times 2.5 \times 17.5 \\
& =962.5 \text { sq. } cm
\end{aligned}
$

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Question 74 Marks

Radii of the circles are given below, find their areas.

10.5 cm

Answer

Radius of the circle $(r)=10.5 cm$... [Given]
Area of the circle $=\pi r^2$
$
\begin{aligned}
& =\frac{22}{7} \times(10.5)^2 \\
& =\frac{22}{7} \times 10.5 \times 10.5 \\
& =22 \times 1.5 \times 10.5 \\
& =346.5 \text { sq. } cm
\end{aligned}
$

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Question 84 Marks

Radii of the circles are given below, find their areas.

28 cm

Answer

Radius of the circle $(r)=28 cm \ldots$ [Given]
Area of the circle $=\pi r^2$
$
\begin{aligned}
& =\frac{22}{7} \times(28)^2 \\
& =\frac{22}{7} \times 28 \times 28 \\
& =22 \times 4 \times 28 \\
& =2464 \text { sq. cm }
\end{aligned}
$

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Maths 4 Mark Question

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