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Match the following:
| Column-I | Column-II |
| (P) A cylindrical roller is of length $ 2 \mathrm{~m} $ and diameter $ 84 \mathrm{~cm} $. The number of revolutions it has to make to cover an area of $ 7920 \mathrm{~m}^{2} $ is | (i) 17600 |
| (Q) The circumference of the base of a right circular cylinder is $ 176 \mathrm{~cm} $. If the height of the cylinder is $ 1 \mathrm{~m} $, the lateral surface area (in sq. $ \mathrm{cm} $ ) of the cylinder is | (ii) 1500 |
| (R) The dimensions of a cuboid are (iii) 9 in the ratio $ 5: 2: 1 $. Its volume is 1250 cubic metres. Its total surface area (in sq. $ \mathrm{m} $ ) is | (iii) 9 |
| (S) If the total surface area of a cubical tank is 486 sq. $ \mathrm{m} $, the length (in $ \mathrm{m} $ ) of one side is | (iv) 850 |
P.
A cylindrical roller is of length \( 2 \mathrm{~m} \) and diameter \( 84 \mathrm{~cm} \).
Radius $=\frac{84}{2\times100}\ m$
$=\frac{42}{100}\ m=0.42\ m$
Curved surface of the cylindrical roller $=2\pi rh$
$=2\times\frac{22}{7}\times 0.42 \times 2$
$=88\times0.06$
$=5.28\ m^2$
Number of revolutions taken by the cylinder$=\frac{Total\ area\ covered\ by\ the\ roller}{Curved\ surface\ of\ the\ cylindrical\ roller}$
$=\frac{7920}{5.28}$
$=1500$
Q.
The circumference of the base of a right circular cylinder is \( 176 \mathrm{~cm} \). The height of the cylinder is \( 1 \mathrm{~m} \),
Circumference of the base $= 2 \pi r$
$176 = 2 \times \frac{22}{7} \times r$
$r=\frac{176\times7}{44}$
$r= 28\ cm$
Height $= 1\ m = 100\ cm$
The lateral surface area of a cylinder $= 2 \pi rh$
$=176 \times 100\ cm^2$
$=17600\ cm^2$
R.
The dimensions of a cuboid are in the ratio \( 5: 2: 1 \). Its volume is 1250 cubic metres.
Let $l=5x, b=2x$ and $h=x$.
Volume of a cuboid of dimensions $l, b$ and $h$ is $lbh$.
Therefore,
$1250=5x \times 2x \times x$
$1250=10x^3$
$x^3=125$
$x^3=5^3$
$x=5$
This implies,
$l=5x=5(5)=25\ cm, b=2x=2(5)=10\ cm, h=x=5\ cm$
Total surface area of the cuboid $=2(lb+bh+lh)$
$=2[25(10)+10(5)+5(25)]$
$=2(250+50+125)$
$=2(425)$
$=850\ cm$
S.
The total surface area of a cubical tank is 486 sq. \( \mathrm{m} \).
Let the side of the tank be $x\ m$.
Total surface area of a cube of length $x$ is $6x^2$
Therefore,
$6x^2=486$
$x^2=81$
$x^2=9^2$
$x=9\ m$
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