Question

Find the curved surface area and volume of a cylinder whose height and radius are (a)15 cm and 4 cm respectively. (b) 17cm and 5.5cm respectively.
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Answer 1

✬ CSA = 377.14 cm², 587.71 cm² ✬

✬ Vol. = 754.28 cm³, 1616.21 cm³ ✬

Step-by-step explanation:

Given:

• Height and radius of first cylinder is 15 cm & 4 cm respectively.
• Height and radius of second cylinder is 17 cm and 5.5 cm respectively.

To Find:

• What is the CSA & Volume of both cylinders ?

Solution: As we know that

★ CSA of Cylinder = 2πrh ★

• Taking π = 22/7

• Height = 15 cm

• Radius = 4 cm

➨ CSA¹ = 2 × 22/7 × 15 × 4 cm²

➨ 44/7 × 60 cm²

➨ 2640/7 cm²

➨ 377.14 cm²

For second cylinder

• Height = 17 cm

• Radius = 5.5 cm

➨ CSA = 2 × 22/7 × 17 × 5.5 cm²

➨ 44/7 × 93.5 cm²

➨ 4114/7 cm²

➨ 587.71 cm²

★ Volume of Cylinder = πr²h ★

• Taking π = 22/7

➼ Volume¹ = 22/7 × 15 × 4 × 4 cm³

➼ 22/7 × 60 × 4 cm³

➼ 5280/7 cm³

➼ 754.28 cm³

For second cylinder

➼ Volume = 22/7 × 17 × 5.5 × 5.5 cm³

➼ 22/7 × 93.5 × 5.5 cm³

➼ 11313.5/7 cm³

➼ 1616.21 cm³

Hence, we got curved surface areas and volumes of both cylinders respectively.

Answer 2

Answer:

Given :-

• (a) Height is 15 cm and radius is 4 cm.
• (b) Height is 17 cm and radius 5.5 cm.

To Find :-

• What is the curved surface area and volume.

Formula Used :-

$\clubsuit$ Curved Surface Area or CSA of Cylinder :

$\longmapsto \sf\boxed{\bold{\pink{Curved\: Surface\: Area =\: 2{\pi}rh}}}$

$\clubsuit$ Volume of Cylinder :

$\longmapsto \sf\boxed{\bold{\pink{Volume\: of\: Cylinder =\: {\pi}{r}^{2}h}}}$

Solution :-

${\small{\bold{\green{\underline{\dashrightarrow\: (a)\: Height =\: 15\: cm\: and\: radius =\: 4\: cm}}}}}$

$\Rightarrow\: \sf\bold{\purple{Curved\: Surface\: Area\: of\: Cylinder\: :-}}$

Given :

• Height = 15 cm
• Radius = 4 cm
• π = 22/7 or 3.14

According to the question by using the formula we get,

$\dashrightarrow$ Curved Surface Area of Cylinder :

$\implies \sf 2 \times \dfrac{22}{7} \times 15 \times 4$

$\implies \sf \dfrac{44}{7} \times 60$

$\implies \sf \dfrac{\cancel{2640}}{\cancel{7}}$

$\implies\sf\bold{\red{377.14\: cm^2}}$

Hence, the curved surface area of cylinder is 377.14 cm².

$\Rightarrow \sf\bold{\purple{Volume\: of\: Cylinder\: :-}}$

Given :

• Height = 15 cm
• Radius = 4 cm

According to the question by using the formula we get,

$\dashrightarrow$ Volume of Cylinder :

$\implies \sf \dfrac{22}{7} \times {(4)}^{2} \times 15$

$\implies \sf \dfrac{22}{7} \times 16 \times 15$

$\implies \sf \dfrac{22}{7} \times 240$

$\implies \sf \dfrac{\cancel{5280}}{\cancel{7}}$

$\implies \sf \bold{\red{754.28\: {cm}^{3}}}$

Hence, the volume of cylinder is 754.28 cm³.

$\rule{150}{2}$

${\small{\bold{\green{\underline{(b)\: Height =\: 17\: cm\: and\: radius =\: 5.5\: cm}}}}}$

$\Rightarrow\sf\bold{\purple{Curved\: Surface\: Area\: of\: Cylinder\: :-}}$

Given :

• Height = 17 cm
• Radius = 5.5 cm

According to the question by using the formula we get,

$\dashrightarrow$ Curved Surface Area of Cylinder :

$\implies \sf 2 \times \dfrac{22}{7} \times 5.5 \times 17$

$\implies \sf \dfrac{44}{7} \times 93.5$

$\implies \sf \dfrac{\cancel{4114}}{\cancel{7}}$

$\implies \sf\bold{\red{587.71\: cm^2}}$

Hence, the curved surface area of cylinder is 587.71 cm².

$\Rightarrow \sf\bold{\purple{Volume\: of\: Cylinder\: :-}}$

Given :

• Height = 17 cm
• Radius = 5.5 cm

According to the question by using the formula we get,

$\dashrightarrow$ Volume of Cylinder :

$\implies \sf \dfrac{22}{7} \times {(5.5)}^{2} \times 17$

$\implies \sf \dfrac{22}{7} \times 30.25 \times 17$

$\implies \sf \dfrac{22}{7} \times 514.25$

$\implies \sf \dfrac{\cancel{11313.5}}{\cancel{7}}$

$\implies \sf\bold{\red{1616.21\: cm^{3}}}$

Hence, the volume of cylinder is 1616.21 cm³.