Radius and height of a conical tent are 7 mts and 10mts respectively,

1.	Radius and height of a conical tent are 7 mts and 10mts respectively, then the areaA. 286.4 mt2B. 268.4 mt2c. 256.3 mt?
Answer» ANSWER: Given: A conical tent of radius = 7m height = 10m To FIND: Area of the tent Diagram: $\setlength{\unitlength}{1.5mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(14,-0.5){\sf{7m}}\put(7.9,9){\sf{10m}}\put(14,25){\sf{\Large{A}}}\put(10,-3){\sf{\Large{B}}}\put(25.5,-3){\sf{\Large{C}}}\end{picture}$ Solution: As we are given a conical tent the area to be taken is lateral(curved) surface area. We know that, ⇒ Lateral Surface Area of a cone = πRl Here, r is radius and l is slant height. In the diagram, slant height is AC. ⇒ Slant height =√(radius²+height²) ⇒ l = √(7²+10²) ⇒ l = √(149) ≈ 12.20m Now, ⇒ Lateral Surface Area of the conical tent = πrl Here, π=22/7; r=7; l=12.20. So, ⇒ Lateral Surface Area of the conical tent = (22/7 * 7 * 12.20)m² ⇒ Lateral Surface Area of the conical tent = (2212.20)m² ⇒ Lateral Surface Area of the conical tent = 268.4m²(option B) Formula Used: Lateral Surface Area of the conical tent = πr*l Learn More: Volume of CYLINDER = πr²h T.S.A of cylinder = 2πrh + 2πr² Volume of cone = ⅓ πr²h C.S.A of cone = πrl T.S.A of cone = πrl + πr² Volume of cuboid = l × b × h C.S.A of cuboid = 2(l + b)h T.S.A of cuboid = 2(LB + bh + lh) C.S.A of cube = 4a² T.S.A of cube = 6a² Volume of cube = a³ Volume of sphere = (4/3)πr³ Surface area of sphere = 4πr² Volume of hemisphere = ⅔ πr³ C.S.A of hemisphere = 2πr² T.S.A of hemisphere = 3πr²

Radius and height of a conical tent are 7 mts and 10mts respectively, then the areaA. 286.4 mt2B. 268.4 mt2c. 256.3 mt?

Answer»

ANSWER:

Given:

A conical tent of radius = 7m
height = 10m

To FIND:

Area of the tent

Diagram:

$\setlength{\unitlength}{1.5mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(14,-0.5){\sf{7m}}\put(7.9,9){\sf{10m}}\put(14,25){\sf{\Large{A}}}\put(10,-3){\sf{\Large{B}}}\put(25.5,-3){\sf{\Large{C}}}\end{picture}$

Solution:

As we are given a conical tent the area to be taken is lateral(curved) surface area.

We know that,

⇒ Lateral Surface Area of a cone = π*R*l

Here, r is radius and l is slant height.

In the diagram, slant height is AC.

⇒ Slant height =√(radius²+height²)

⇒ l = √(7²+10²)

⇒ l = √(149) ≈ 12.20m

Now,

⇒ Lateral Surface Area of the conical tent = π*r*l

Here, π=22/7; r=7; l=12.20. So,

⇒ Lateral Surface Area of the conical tent = (22/7 * 7 * 12.20)m²

⇒ Lateral Surface Area of the conical tent = (22*12.20)m²

⇒ Lateral Surface Area of the conical tent = 268.4m²(option B)

Formula Used:

Lateral Surface Area of the conical tent = π*r*l

Learn More:

Volume of CYLINDER = πr²h
T.S.A of cylinder = 2πrh + 2πr²
Volume of cone = ⅓ πr²h
C.S.A of cone = πrl
T.S.A of cone = πrl + πr²
Volume of cuboid = l × b × h
C.S.A of cuboid = 2(l + b)h
T.S.A of cuboid = 2(LB + bh + lh)
C.S.A of cube = 4a²
T.S.A of cube = 6a²
Volume of cube = a³
Volume of sphere = (4/3)πr³
Surface area of sphere = 4πr²
Volume of hemisphere = ⅔ πr³
C.S.A of hemisphere = 2πr²
T.S.A of hemisphere = 3πr²