The volume of a solid cylinder is 448 \pi \ cm^3 and height 7 \ cm . Find its lateral surface area and total surface area.

Let the radius of the base and height of the cylinder be r cm and h cm respectively. Then, h=7 \ cm Now, Volume = 448\pi \ cm^3 \pi r^2h=448 \pi r^2=\dfrac{448}{7}=64 r=8 \ cm Therefore,Lateral surface area =2\pi rh =2\times \dfrac{22}{7}\times 8 \times 7 Lateral surface area =352 \ cm^2 Total surface area =2\pi r(r+h)=2\times \dfrac{22}{7} \times 8(7+8) Total surface area =\dfrac{5280}{7} Total surface area =754.28 \ cm^2

Total surface area of cylinder is 60\pi\ cm^ {2} and its height 7\ cm . Find the curved surface area of cylinder.

As we know that,Total surface area of cylinder = 2 \pi r h + 2 \pi {r}^{2} = 60 \pi \; {cm}^{2} \quad \left( \text{Given} \right) Therefore, 2 \pi {r}^{2} + 2 \pi \cdot r \cdot 7 = 60 \pi\\ {r}^{2} + 7r = 30\\ {r}^{2} + 7r - 30 = 0\\ {r}^{2} + 10r - 3r - 20 = 0\\ \left( r + 10 \right) \left( r - 3 \right) = 0\\ \because r \ne -ve\\ \therefore r = 3 \; cm Therefore,Curved surface area of cylinder = 2 \pi r h \\ = 2 \times \pi \times 3 \times 7 = 42 \pi \; {cm}^{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: 12 cylindrical pillars of a building have to be cleaned.If the diameter of each pillar is 42 cm and the height of each pillar is 5 m, what will be the cost of cleaning these at the rate of Rs. 5 per sq.m

Diameter of pillar =42 cmRadius =r=\dfrac{42}{2}=21 cm =\dfrac{21}{100} mCurved area of pillar =2\pi rh=2\times\dfrac{22}{7}\times\dfrac{21}{100} \times 5=6.6 sq.mTotal area of 12 pillars =12\times 6.6 sq.m =79.2 sq.mCost of cleaning for 1 sq.m = Rs. 5 Cost of cleaning for 79.2 sq.m = Rs. 5\times 79.2= Rs. 396 \therefore Cost of cleaning for 79.2 sq.m Rs.396

Q: Find the radius of the cylinder if the area of its curved surface area is 352 sq.cm and its height is 16 cm

Given : Height =16 cmCurved surface area =352 sq.cmWe know that, \Rightarrow Curved Surface area =2\pi rh \therefore 2\pi r h=352 \Rightarrow 2\times\dfrac{22}{7}\times r\times 16=352 \Rightarrow r=352\times\dfrac{1}{2}\times\dfrac{7}{22}\times\dfrac{1}{16}=\dfrac{7}{2}=3.5 cm \therefore Radius of the cylinder =3.5 cm

Q: The volume of a cylinder of height 8\ cm is 1232\ cm^{3} . Find its curved surface area and total surface area.

Given that height of the cylinder is 8\ cm and volume is 1232\ cm^{3} We know that the volume of the cylinder =\pi r^{2}h So, 1232=22/7\times r\times r\times 8 r^{2}=1232\times 7/8 r=7\ cm Also we know that curved surface area of cylinder =2\pi rh So,Curved surface area =2\times 22/7\times 7\times 8 Curved surface area =252\ cm^{2} We know that total surface area of cylinder =2\pi r(r+h) So,Total surface area =2\times 22/7\times 7(7+8) Total surface area =2580\ cm^{2}

Q: Find the volume, curved surface area and total surface area of a cylinder whose dimensions are, radius of the base =7\ cm and height =50\ cm

We know that volume of the cylinder =\pi r^2h Here r=7\ cm\ h=50\ cm So, V=22/7\times 7\times 7\times 50 V=22\times 7\times 50 V=7700\ cm^3 Also we know that curved surface area of cylinder =2\pi rh So,Curved surface area =2\times 22/7 \times 7\times 50 Curved surface area =2200\ cm^2 We know that total surface area of cylinder =2\pi (r+h) So,Total surface area =2\times 22/7 \times 7(7+50) Total surface area =2580\ cm^2

Q: Find the volume, curved surface area and total surface area of a cylinder whose dimensions are radius of the base =5.6\ m and height =1.25\ m

We know that volume of the cylinder =\pi r^2h Here r=5.6\ m\ h=1.25\ m So, V=22/7\times 5.6\times 5.6\times 1.25 V=123.2\ m^3 Also we know that curved surface area of cylinder =2\pi rh So,Curved surface area =2\times 22/7 \times 5.6\times 1.25 Curved surface area =44\ m^2 We know that total surface area of cylinder =2\pi (r+h) So,Total surface area =2\times 22/7 \times 5.6(5.6+1.25) Total surface area =241.12\ m^2

Q: The radius and height of a cylinder area in the ratio 7:2 . If the volume of the cylinder is 8316\ cm^{3} , find the surface area of cylinder.

Given that radius and height of a cylinder are in the ratio 7:2 Hence radius / height =7/2 r=(7/2)h We know that the volume of the cylinder =\pi r^{2}h So, 8316=22/7\times (7/2)h\times (7/2)h\times h h^{3}=216 h=6\ cm Therefore r=(7/2)\times 6=21\ cm We know that total surface area of cylinder =2\pi r(r+h) So,Total surface area =2\times 22/7\times 21(21+6) Total surface area =3564\ cm^{2}

Q: Find the volume, curved surface area and total surface area of a cylinder whose dimensions are radius of the base =14\ dm and height =15\ m

We know that volume of the cylinder =\pi r^2h Here r=14\ dm=1.4\ m,\ h=15\ m So, V=22/7\times 1.4\times 1.4\times 15 V=92.4\ m^3 Also we know that curved surface area of cylinder =2\pi rh So,Curved surface area =2\times 22/7 \times 1.4\times 15 Curved surface area =132\ m^2 We know that total surface area of cylinder =2\pi (r+h) So,Total surface area =2\times 22/7 \times 1.4(1.4+15) Total surface area =144.32\ m^2

Q: The total surface area of a circular cylinder is 1540 sq.cm.If the height is four times the radius of the base , find the height of the cylinder.

Height =4\times radius of the base. \Rightarrow h=4r where r is the radius of the baseTotal surface area =1540 sq.cm 2\pi r\left(r+h\right)=1540 \Rightarrow 2\pi r\left(r+4r\right)=1540 \Rightarrow 2\times\dfrac{22}{7}\times 5{r}^{2}=1540 \Rightarrow {r}^{2}=\dfrac{1540\times 7}{22\times 10}=49 \therefore r=7 Hence height =h=4r=4\times 7=28 cm

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Important questions on Surface Area Of Right Circular Cylinders And Cones

12 cylindrical pillars of a building have to be cleaned.If the diameter of each pillar is 42cm and the height of each pillar is 5m, what will be the cost of cleaning these at the rate of Rs.5 per sq.m

Find the radius of the cylinder if the area of its curved surface area is 352sq.cm and its height is 16cm

The volume of a cylinder of height 8 cm is 1232 cm3. Find its curved surface area and total surface area.

The volume of a solid cylinder is 448π cm3 and height 7 cm. Find its lateral surface area and total surface area.

Find the volume, curved surface area and total surface area of a cylinder whose dimensions are, radius of the base =7 cm and height =50 cm

Find the volume, curved surface area and total surface area of a cylinder whose dimensions are radius of the base =5.6 m and height =1.25 m

The radius and height of a cylinder area in the ratio 7:2. If the volume of the cylinder is 8316 cm3, find the surface area of cylinder.

Find the volume, curved surface area and total surface area of a cylinder whose dimensions are radius of the base =14 dm and height =15 m

The total surface area of a circular cylinder is 1540sq.cm.If the height is four times the radius of the base , find the height of the cylinder.

Total surface area of cylinder is 60π cm2 and its height 7 cm. Find the curved surface area of cylinder.

More important questions

$12$ cylindrical pillars of a building have to be cleaned.If the diameter of each pillar is $42$ cm and the height of each pillar is $5$ m, what will be the cost of cleaning these at the rate of Rs. $5$ per sq.m

Find the radius of the cylinder if the area of its curved surface area is $352$ sq.cm and its height is $16$ cm

The volume of a cylinder of height $8 c m$ is $1232 c m^{3}$ . Find its curved surface area and total surface area.

The volume of a solid cylinder is $448 π c m^{3}$ and height $7 c m$ . Find its lateral surface area and total surface area.

Find the volume, curved surface area and total surface area of a cylinder whose dimensions are, radius of the base $= 7 c m$ and height $= 50 c m$

Find the volume, curved surface area and total surface area of a cylinder whose dimensions are radius of the base $= 5.6 m$ and height $= 1.25 m$

The radius and height of a cylinder area in the ratio $7 : 2$ . If the volume of the cylinder is $8316 c m^{3}$ , find the surface area of cylinder.

Find the volume, curved surface area and total surface area of a cylinder whose dimensions are radius of the base $= 14 d m$ and height $= 15 m$

The total surface area of a circular cylinder is $1540$ sq.cm.If the height is four times the radius of the base , find the height of the cylinder.

Total surface area of cylinder is $60 π c m^{2}$ and its height $7 c m$ . Find the curved surface area of cylinder.