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Answer 1

Question 1 :-

$\red{★}$The water tank is in the cylindrical shape and the diameter of its base is 28 cm. if it is 7 metres Deep, how many kilolitres of water it can hold?

Given :-

• The diameter of the base of the cylinder = 28 m.

• Height = 7 m.

To Find :-

• How many kilolitres of water can it hold.

Solution :-

$\blue{★}$Formula to find the volume of the cylinder :-

${\boxed{{\bf{\:V = \pi r ^{2}h }}}}$

${\bf\red{⟹\: r = radius \: of \: cylinder}}$

${\bf\red{⟹\: r = 14}}$

$\blue{★}$Putting all the values of the above formula we get:-

${\bf\green{ ⟶\:V = \frac{22}{7} \times {14}^{2} \times 7 }}$

${\bf\green{ ⟶\:V = 4312 \: {m}^{3} }}$

Since,

${\bf\orange{➯\: 1 \: {m}^{3} = 1 \: kl}}$

So,

${\bf\orange{➯\: 4312 \: {m}^{3} = 4312 \: kl}}$

∴ So, the cylinder can hold 4312 kl of water.

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Question 2 :-

$\red{★}$A rectangular sheet of paper is rolled along its length to make a cylinder.the sheet is 33 cm long and 32 cm wide a circular sheet of paper is attached to the bottom of the cylinder formed.

Given :-

• Length of the rectangular sheet = 33 cm.

• Width of the rectangular sheet = 32 cm.

To Find :-

• Capacity or volume of the cylinder.

Solution :-

$\blue{★}$Length of the rectangular sheet = Circumference of the circle.

${\boxed{{\bf{</p><p>Circumference \: of \: the \: circle = 2\pi r}}}}$

${\bf{→ 33 \: cm = \frac{2 \times 22}{7 \times r} }}$

${\bf{→ r = \frac{33 \times 7}{22 \times 2} }}$

${\bf{→ r = \frac{231}{44} }}$

$\pink{\bf{→ r = 5.25 \: cm }}$

${\boxed{{\bf{Capacity \: or \: volume \: of \: the \: cylinder = \pi {r}^{2} h}}}}$

${\bf{→ \frac{22}{7 \times 5.25 \times 5.25 \times 32} }}$

${\bf{→ \frac{22}{7 \times 27 .5625 \times 32} }}$

${\bf{→ \frac{19404}{7} }}$

$\purple{\bf{→ 2772 \: {cm}^{3} }}$

$\blue{★}$Hence, the capacity or volume of the cylinder = 2772 cm³.

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Question 3 :-

$\green{★}$The thickness of a hollow metallic cylinder is 2 cm It is 35 cm long and its inner radius is 12 cm.Find the volume of metal required to make the cylinder assuming it is open and the other end.

Given :-

• Inner radius of cylinder r = 12 cm.

• Thickness = 2 cm.

• Height = 35 cm.

To Find :-

• Other radius.

• Volume of metal required to make cylinder.

Solution :-

• Other radius R = ${\bf{12 + 2 = 14 \: cm }}$

• It is a hollow cylinder.

${\boxed{{\bf{Volume \: of \: metal \: required \: to \: make \: cylinder = outer \: volume - inner \: volume}}}}$

${\bf{→ \pi R^{2} h - \pi r ^{2} h }}$

${\bf{→ \frac{22}{7} \times 35 \times (14 ^{2} - 12 ^{2}) }}$

${\bf\red{→ {5720 \: cm}^{2} }}$

$\green{★}$Hence, the volume of metal required to make the cylinder, assuming it is open, at either end = ${\bf{ {5720 \: cm}^{2} }}$

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Question 4 :-

$\red{★}$The volume of a cylinder is ${ 150\pi cm^{3}}$ cm and height is 6 cm. Find the areas of it's total surface and (lateral) curved surface.

Given :-

• The volume of cylinder = ${ 150\pi cm^{3}}$

• Height of cylinder = 6 cm.

To Find :-

Find it's TSA (total surface area) and LSA (lateral surface area).

Solution :-

$\blue{★}$Let the radius of cylinder be r cm.

• We know that,

${\boxed{{\bf{Volume \: of \: cylinder = \pi r ^{2}h}}}}$

${\bf{ ➯\:150\pi = \pi r^{2}h }}$

${\bf{ ➯\: \frac{150\pi}{\pi} = r ^{2} (6)}}$

${\bf{ ➯\: \frac{150}{6} = r ^{2} }}$

${\bf{ ➯\: 25 = {r}^{2} }}$

${\bf{ ➯\: \sqrt{25} = {r}}}$

${\bf\green{ ➯\: 5 = {r}}}$

• So, the radius of the cylinder = 5 cm.

${\boxed{{\bf{ ✎\:TSA = 2\pi r(h + r)}}}}$

${\bf{➨\:TSA = 2( \frac{22}{7} )(5)(6 + 5)}}$

${\bf{ ➨\: \frac{44}{7} (5)(11)}}$

${\bf{ ➨\: \frac{44}{7} (55)}}$

${\bf\red{➨\: 345.71 \: {cm}^{2} }}$

${\boxed{{\bf{✎ \:LSA = 2\pi rh }}}}$

${\bf{➨\: LSA = 2( \frac{22}{7} )(5)(6)}}$

${\bf{➨\: \frac{44}{7} (30)}}$

${\bf{➨\: \frac{1320}{7} }}$

${\bf\red{➨\: 188.57 \: cm ^{2} }}$