Question

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. 256.3 mt?​

Answer 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

$\implies \sf \dfrac{22}{7} \times 7 \times 12.20$

Cancelling,

$\implies \sf \dfrac{22}{\not7} \times\not 7 \times 12.20$

⇒ 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 = $\sf \dfrac{1}{3} \pi r^{2} h$

Answer 2

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