A metal pipe is 77 cm77 cm long. The inner diameter of a cross-section is 4 cm4 cm, the outer diameter being 4.4 cm4.4 cm, then find its total surface area.

Dimensions be : \Rightarrow R= Outer radius =\dfrac{4.4}{2}=2.2cm r= Inner radius \dfrac{4}{2}=2cm Height h=77cm \Rightarrow Inner curved surface area =2\pi rh =2\times \dfrac{22}{7}\times 2\times 77 =968cm^2 \Rightarrow Outer curved surface area =2\pi Rh =2\times \dfrac{22}{7}\times 4.2\times 77 =1064.8cm^2 \Rightarrow Total surface area =968+1064.8+2\pi \times \;Ring's\;area =968+1064.8+2\times \left[ \pi { R }^{ 2 }-\pi { r }^{ 2 } \right] =968+1064.8 +2\times \left[ \dfrac { 22 }{ 7 } \times { \left( 2.2 \right) }^{ 2 }-\dfrac { 22 }{ 7 } \times { \left( 2 \right) }^{ 2 } \right] =968+1064.8+2\times \dfrac{22}{7} \times \left[ { \left( 2.2 \right) }^{ 2 }-{ \left( 2 \right) }^{ 2 } \right] =968+1064.8 +5.28 =2038.08 \Rightarrow Total surface area =2038.08cm^2. Hence, the answer is 2038.08cm^2.

A metal pipe is 77 cm77 cm long. The inner diameter of a cross-section is 4 cm4 cm, the outer diameter being 4.4 cm,4.4 cm then find its outer curved surface area.

Dimensions be : \Rightarrow R= outer radius =\dfrac{4.4}{2}=2.2cm r= Inner radius =\dfrac{4}{2}=2cm \Rightarrow Height h=77cm \therefore Outer curved surface area =2\pi Rh =2\times \dfrac{22}{7}\times 2.2\times 77 =1064.8cm^2 \therefore Outer curved surface area =1064.8cm^2. Hence, the answer is 1064.8cm^2.

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9th
Maths
Surface Areas and Volumes
Surface Area of Right Circular Cylinders and Cones
$Surface Area Of Right Circu...$

Important questions on Surface Area Of Right Circular Cylinders And Cones

Q: A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5 , show that the radius of each is to the height of each as 3:4 .

For cylinder, we havebase radius = r, height = h \therefore S_1= Curved surface =2\pi rh For cone, we have l=\sqrt{r^2+h^2} and, S_2=\pi rl=\pi r\sqrt{r^2+h^2} We have, \dfrac{S_1}{S_2}=\dfrac{8}{5} \Rightarrow \dfrac{2\pi rh}{\pi r\sqrt{r^2+h^2}}=\dfrac{8}{5} \Rightarrow \dfrac{2h}{\sqrt{r^2+h^2}}=\dfrac{8}{5} \Rightarrow \dfrac{4h^2}{r^2+h^2}=\dfrac{64}{25} \Rightarrow 25h^2=16r^2+16h^2\Rightarrow 9h^2=16r^2\Rightarrow 3h=4r \Rightarrow \dfrac{r}{h}=\dfrac{3}{4} .

Q: The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metel used in making the cylinder assuming that it is open at both the ends Also find its weight if the metal weighdds 8 g per cm3.

Let t is thickness of the cylinder { r }_{ 1 } is outer radius of the cylinder { r }_{ 2 } is inner radius of the cylinder h is height of the cylinder \therefore t=2 cm { r }_{ 1 }=14 cm h=70 cm Now, inner radius is calculated as, { r }_{ 2 }={ r }_{ 1 }-t \therefore { r }_{ 2 }=14-2=12 cm 1) Volume of the hollow cylinder is given by, V=c/s\quad area\times height\quad of\quad cylinder \therefore V=\left( \pi { { r }_{ 1 } }^{ 2 }-\pi { { r }_{ 2 } }^{ 2 } \right) \times h \therefore V=\pi \left( 14^{ 2 }-12^{ 2 } \right) \times 70 \therefore V=\frac { 22 }{ 7 } \left( 196-144 \right) \times 70 \therefore V=22\times 52\times 10 \therefore V=11440\quad { cm }^{ 3 } 2) Given wright of the metal, \rho =8\quad \frac { g }{ { cm }^{ 3 } } Let m = mass of the cylinder \therefore \rho =\frac { m }{ V } \therefore 8=\frac { m }{ 11440 } \therefore m=8\times 11440 \therefore m=91520 gm \therefore m=91.520 kg

Q: If radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 5 : 6 , find the ratio of their curved surfaces.

\cfrac { { S }_{ 1 } }{ { S }_{ 2 } } =\cfrac { 2\pi { r }_{ 1 }{ h }_{ 1 } }{ 2\pi { r }_{ 2 }{ h }_{ 2 } } =\cfrac { 4\times 5 }{ 3\times 6 } =\cfrac { 10 }{ 9 } =10:9

Q: What length of solid cylinder 2 cm in diameter must be taken to cast into a hollow cylinder of external diameter 12 cm, 0.25 cm thick and 15 cm long ?

Volume of solid cylinder = Volume of hollow cylinder \Rightarrow \pi { r }^{ 2 }h=\pi \left( { \left( 6 \right) }^{ 2 }-{ \left( 6-0.25 \right) }^{ 2 } \right) \times 15 \Rightarrow { (1) }^{ 2 }\times h=\left( 36-33.0625 \right) \times 15 h=44.0625 \therefore Length of solid cylinder =440.625cm

Q: The diameter of a garden roller is 1.4m and it is 2m long. How much area will it cover in 5 revolution?

Diameter = 1.4 mr = d/2r = 1.4/2r = 0.7 mcurved surface area of cylinder = 2^{\ast }22/7^{\ast }r\wedge 2 = 2^{\ast }22/7^{\ast }0.7^{\ast } 0.7 =8.8m^{\wedge }2 No of revolution = 5Therefore =8.8^{\ast }5 = 44 m2

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A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm, then find its total surface area.

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HARD

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio $8 : 5$ , show that the radius of each is to the height of each as $3 : 4$ .

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HARD

The diameter of a cylinder is $28 c m$ and its heights is $40 c m$ . Find the curved surface area, total surface area and the volume of the cylinder.

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HARD

The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metel used in making the cylinder assuming that it is open at both the ends Also find its weight if the metal weighdds 8 g per cm3.

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HARD

A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm, then find its outer curved surface area.

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HARD

If radii of two cylinders are in the ratio $4 : 3$ and their heights are in the ratio $5 : 6$ , find the ratio of their curved surfaces.

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HARD

What length of solid cylinder $2$ cm in diameter must be taken to cast into a hollow cylinder of external diameter $12$ cm, $0.25$ cm thick and $15$ cm long ?

$44.0123$ cm

$42.3215$ cm

$44.0625$ cm

$44.6023$ cm

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HARD

The diameter of a garden roller is $1.4 m$ and it is $2 m$ long. How much area will it cover in $5$ revolution?

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Important questions on Surface Area Of Right Circular Cylinders And Cones

A metal pipe is 77 cm77 cm long. The inner diameter of a cross-section is 4 cm4 cm, the outer diameter being 4.4 cm4.4 cm, then find its total surface area.

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.

The diameter of a cylinder is 28 cm and its heights is 40 cm. Find the curved surface area, total surface area and the volume of the cylinder.

The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metel used in making the cylinder assuming that it is open at both the ends Also find its weight if the metal weighdds 8 g per cm3.

A metal pipe is 77 cm77 cm long. The inner diameter of a cross-section is 4 cm4 cm, the outer diameter being 4.4 cm,4.4 cm then find its outer curved surface area.

If radii of two cylinders are in the ratio 4:3 and their heights are in the ratio 5:6, find the ratio of their curved surfaces.

What length of solid cylinder 2 cm in diameter must be taken to cast into a hollow cylinder of external diameter 12 cm, 0.25 cm thick and 15 cm long ?

44.0123 cm

42.3215 cm

44.0625 cm

44.6023 cm

The diameter of a garden roller is 1.4m and it is 2m long. How much area will it cover in 5 revolution?

More important questions

A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm, then find its total surface area.

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio $8 : 5$ , show that the radius of each is to the height of each as $3 : 4$ .

The diameter of a cylinder is $28 c m$ and its heights is $40 c m$ . Find the curved surface area, total surface area and the volume of the cylinder.

A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm, then find its outer curved surface area.

If radii of two cylinders are in the ratio $4 : 3$ and their heights are in the ratio $5 : 6$ , find the ratio of their curved surfaces.

What length of solid cylinder $2$ cm in diameter must be taken to cast into a hollow cylinder of external diameter $12$ cm, $0.25$ cm thick and $15$ cm long ?

$44.0123$ cm

$42.3215$ cm

$44.0625$ cm

$44.6023$ cm

The diameter of a garden roller is $1.4 m$ and it is $2 m$ long. How much area will it cover in $5$ revolution?