Question

if area of hemisphere is 28,000m2 find the diameter of hemisphere​

Answer 1

Answer :

›»› The diameter of a hemisphere is 133.54 m.

Step-by-step explanation :

Given :

• Area of a hemisphere = 28000 m².

To Find :

• Diameter of a hemisphere = ?

Knowledge required :

First we will find the radius of a hemisphere, after that we will find the diameter of a hemisphere.

To find the radius of a hemisphere we use the formula of a hemisphere.

Formula of area of hemisphere to calculate the radius of a hemisphere is given by,

→ Area of hemisphere = 2πr².

Here,

• The value of π is 22/7.
• r is the Radius of a hemisphere.

Units,

• The unit of radius is m.

Formula to calculate the diameter of a hemisphere is given by,

→ D = 2r

Here,

• D is the Diameter of a hemisphere.
• r is the Radius of hemisphere.

Units,

• The unit of Diameter is centimetre (cm).
• The unit of Radius is centimetre (cm).

Solution :

As we are given with area of hemisphere then we know the required formula, that is,

→ Area of hemisphere = 2πr².

By using the formula of area of hemisphere to calculate the radius of a hemisphere and substituting the given values in the formula, we get :

→ 28000 = 2 * 22/7 * r²

→ 28000 = 44/7 * r²

→ 28000 = 6.28 * r²

→ 28000 = 6.28r²

→ r² = 28000/6.28

→ r² = 2800000/628

→ r² = 4458.59

→ r = √4458.59

→ r = 66.77.

Now,

We know that, if we are given with radius of a hemisphere then we have the required formula, that is,

→ D = 2r.

By using the formula to calculate the diameter of hemisphere and substituting the given values in the formula, we get :

→ D = 2 * 66.77

→ D = 133.54.

Hence, the diameter of a hemisphere is 133.54 m.

Answer 2

${\bold{\sf{\underline{Understanding \: the \: question}}}}$

✺ This question says that there is a hemisphere given it's area is 28,000 m² Now we have to find its diameter.

${\bold{\sf{\underline{Given \: that}}}}$

✺ Area of hemisphere = 28,000 m²

${\bold{\sf{\underline{To \: find}}}}$

✺ Diameter of hemisphere.

${\bold{\sf{\underline{Solution}}}}$

✺ Diameter of hemisphere = 133.54 m

${\bold{\sf{\underline{Using \: concept}}}}$

✺ Area of hemisphere formula

✺ Finding radius formula

${\bold{\sf{\underline{Using \: formula}}}}$

✺ Area of hemisphere = 2πr²

✺ Diameter = 2r

${\bold{\sf{\underline{Meanings}}}}$

✺ r means radius.

✺ Diameter as d

✺ π pronounced as pi

✺ Value of π is 22/7

${\bold{\sf{\underline{Converting \: d \: into \: r}}}}$

~ Using formula = 2r

${\bold{\sf{\underline{Full \: solution}}}}$

~ Finding radius

➝ Area = 2πr²

➝ 28000 = 2 × 22/7 × r²

➝ 28000 = 44/7 × r²

➝ 28000 = 6.28 × r²

➝ 28000 / 6.28 = r²

➝ 4458.59 = r²

➝ √4458.59 = r

➝ 66.77 = r

➝ r = 66.77 m

~ Finding diameter

➝ Diameter = 2r

➝ Diameter = 2(66.77)

➝ Diameter = 2 × 66.77

➝ Diameter = 133.54 m

• Henceforth, diameter is 133.54 m

${\red{\sf{\underline{More \: knowledge}}}}$

Diagram of Sphere :

$\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf R}\end{picture}$