radius and height of a conical tent are 7 mts and 10mts respectively, then the area
A. 286.4 mt2
B. 268.4 mt2
c. 25

2 thoughts on “radius and height of a conical tent are 7 mts and 10mts respectively, then the area<br />A. 286.4 mt2<br />B. 268.4 mt2<br />c. 25”

1. Given :-

   • Radius of the conical tent = 7mts
   • Height of the conical tent = 10mts

   Aim :-

   • To find the surface area of the conical tent

   Formula to use :-

   Curved surface area of a cone = πrl

   Here, l is the slant height.

   In order to find the slant height, we have to use the Pythagoras theorem.

   Pythagoras theorem :-

   The Pythagoras theorem states that, the base squared added with the height squared results in hypotenuse squared.

   (base)² + (height)² = (hypotenuse)²

   • radius = base
   • slant height = hypotenuse

   Let the slant height be L.

   ⇒ (7)² + (10)² = L²

   ⇒ 49 + 100 = L²

   ⇒ 149 = L²

   Transposing the power,

   ⇒ √149 = L

   Let us take √149 = 12.20

   Now that we have the value of the slant height,

   substituting,

   ⇒ π × 7 × 12.20

   [tex]\implies \sf \dfrac{22}{7} \times 7 \times 12.20[/tex]

   Cancelling,

   [tex]\implies \sf \dfrac{22}{\not7} \times\not 7 \times 12.20[/tex]

   ⇒ 22 × 12.20

   ⇒ 268.4mts² (approximately)

   Option (b) 268.4 mts² is correct.

   Some more formulas :-

   • Total surface area of a cone = πr² + πrl = πr(l+r)
   • Volume of a cone = [tex]\sf \dfrac{1}{3} \pi r^{2} h[/tex]

   Reply

2. ANSWER:

   Given:

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

   To Find:

   • Area of the tent

   Diagram:

   [tex]\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}[/tex]

   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

   Reply