Question

127 2/7 sqcm of sheet is required to make a hemispherical bowl. Let us write by calculating the length of diameter of the forepart of the bowl.​

Answer 1

Answer:

Given :-

• 127 2/7 sqcm of sheet is required to make a hemisphere bowl.

To Find :-

• What is the length of diameter of the forepart of the bowl.

Formula Used :-

${\red{\boxed{\small{\bold{T.S.A\: of\: a\: hollow\: hemisphere =\: 2{\pi}{r}^{2}}}}}}$

where,

• T.S.A = Total Surface Area

Solution :-

Let, the radius be r cm

According to the question by using the formula we get,

⇒ $\sf 2{\pi}{r}^{2} =\: 127\dfrac{2}{7}$

⇒ $\sf 2{\pi}{r}^{2} =\: \dfrac{889 + 2}{7}$

⇒ $\sf 2 \times \dfrac{22}{7} \times {r}^{2} =\: \dfrac{891}{7}$

⇒ $\sf {r}^{2} =\: \dfrac{891}{7} \times \dfrac{7}{2 \times 22}$

⇒ $\sf {r}^{2} =\: \dfrac{891}{\cancel{7}} \times \dfrac{\cancel{7}}{44}$

⇒ $\sf {r}^{2} =\: \dfrac{\cancel{891}}{\cancel{44}}$

⇒ $\sf {r}^{2} =\: \dfrac{81}{4}$

⇒ $\sf r =\: \sqrt{\dfrac{81}{4}}$

➠ $\sf\bold{\green{r =\: \dfrac{9}{2}\: cm}}$

Now, we have to find the diameter of the forepart of the bowl,

As we know that,

$\mapsto$ $\boxed{\bold{\small{Diameter =\: 2r}}}$

Given :

• Radius (r) = 9/2 cm

According to the question by using the formula we get

↦ $\sf Diameter =\: {\cancel{2}} \times \dfrac{9}{\cancel{2}}$

➦ $\sf\bold{\purple{Diameter =\: 9\: cm}}$

${\underline{\boxed{\small{\bf{\therefore The\: length\: of\: diameter\: of\: the\: forepart\: of\: the\: bowl\: is\: 9\: cm\: .}}}}}$

Answer 2

Given :- 127 2/7 sqcm of sheet is required to make a hemispherical bowl. Let us write by calculating the length of diameter of the forepart of the bowl. ?

Solution :-

we know that,

• curved surface area of a hemispherical bowl is = 2 * π * (radius)² .
• Diameter = 2 * radius .
• Sheet total area = curved surface area of a hemispherical bowl .

Let us assume that, radius of hemisphere is r cm.

so, comparing area , we get,

→ 2 * π * (r)² = 127(2/7)

→ 2 * (22/7) * (r)² = (891/7)

→ 2 * 22 * r² = 891

dividing both sides by 11,

→ 2 * 2 * r² = 81

→ 4r² = 81

→ r² = (81/4)

→ r² = (9/2)²

→ (r)² = (9/2)²

square root both sides,

→ r = (9/2) cm.

therefore,

→ Diameter of hemispherical bowl = 2 * (9/2) = 9 cm. (Ans.)

Hence, the diameter of the forepart of the bowl is 9 cm.

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