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 5.5

2 thoughts on “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 5.5”

1. 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 :-

   [tex]\clubsuit[/tex] Curved Surface Area or CSA of Cylinder :

   [tex]\longmapsto \sf\boxed{\bold{\pink{Curved\: Surface\: Area =\: 2{\pi}rh}}}\\[/tex]

   [tex]\clubsuit[/tex] Volume of Cylinder :

   [tex]\longmapsto \sf\boxed{\bold{\pink{Volume\: of\: Cylinder =\: {\pi}{r}^{2}h}}}\\[/tex]

   Solution :-

   [tex]{\small{\bold{\green{\underline{\dashrightarrow\: (a)\: Height =\: 15\: cm\: and\: radius =\: 4\: cm}}}}}[/tex]

   [tex]\Rightarrow\: \sf\bold{\purple{Curved\: Surface\: Area\: of\: Cylinder\: :-}}[/tex]

   Given :

   Height = 15 cm

   Radius = 4 cm

   π = 22/7 or 3.14

   According to the question by using the formula we get,

   [tex]\dashrightarrow[/tex] Curved Surface Area of Cylinder :

   [tex]\implies \sf 2 \times \dfrac{22}{7} \times 15 \times 4[/tex]

   [tex]\implies \sf \dfrac{44}{7} \times 60[/tex]

   [tex]\implies \sf \dfrac{\cancel{2640}}{\cancel{7}}[/tex]

   [tex]\implies\sf\bold{\red{377.14\: cm^2}}[/tex]

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

   [tex]\Rightarrow \sf\bold{\purple{Volume\: of\: Cylinder\: :-}}[/tex]

   Given :

   Height = 15 cm

   Radius = 4 cm

   According to the question by using the formula we get,

   [tex]\dashrightarrow[/tex] Volume of Cylinder :

   [tex]\implies \sf \dfrac{22}{7} \times {(4)}^{2} \times 15[/tex]

   [tex]\implies \sf \dfrac{22}{7} \times 16 \times 15[/tex]

   [tex]\implies \sf \dfrac{22}{7} \times 240[/tex]

   [tex]\implies \sf \dfrac{\cancel{5280}}{\cancel{7}}[/tex]

   [tex]\implies \sf \bold{\red{754.28\: {cm}^{3}}}[/tex]

   Hence, the volume of cylinder is 754.28 cm³.

   [tex]\rule{150}{2}[/tex]

   [tex]{\small{\bold{\green{\underline{(b)\: Height =\: 17\: cm\: and\: radius =\: 5.5\: cm}}}}}[/tex]

   [tex]\Rightarrow\sf\bold{\purple{Curved\: Surface\: Area\: of\: Cylinder\: :-}}[/tex]

   Given :

   Height = 17 cm

   Radius = 5.5 cm

   According to the question by using the formula we get,

   [tex]\dashrightarrow[/tex] Curved Surface Area of Cylinder :

   [tex]\implies \sf 2 \times \dfrac{22}{7} \times 5.5 \times 17[/tex]

   [tex]\implies \sf \dfrac{44}{7} \times 93.5[/tex]

   [tex]\implies \sf \dfrac{\cancel{4114}}{\cancel{7}}[/tex]

   [tex]\implies \sf\bold{\red{587.71\: cm^2}}[/tex]

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

   [tex]\Rightarrow \sf\bold{\purple{Volume\: of\: Cylinder\: :-}}[/tex]

   Given :

   Height = 17 cm

   Radius = 5.5 cm

   According to the question by using the formula we get,

   [tex]\dashrightarrow[/tex] Volume of Cylinder :

   [tex]\implies \sf \dfrac{22}{7} \times {(5.5)}^{2} \times 17[/tex]

   [tex]\implies \sf \dfrac{22}{7} \times 30.25 \times 17[/tex]

   [tex]\implies \sf \dfrac{22}{7} \times 514.25[/tex]

   [tex]\implies \sf \dfrac{\cancel{11313.5}}{\cancel{7}}[/tex]

   [tex]\implies \sf\bold{\red{1616.21\: cm^{3}}}[/tex]

   Hence, the volume of cylinder is 1616.21 cm³.

   Reply

2. Radius of cylinder (r)=7cm

   Height of cylinder (h)=15cm

   Curved Surface Area =2πrh

   =2×(22/7)×7×15

   =660cm2

   Total Surface Area =2πr(h+r)

   =2×(22/7)×7(15+7)

   =2×22×22

   =968cm2

   Reply