Question

14. A hemispherical bowl is made of steel, 0.25 cm thick.
The inner radius of the bowl is 5 cm. Find the outer
curved surface area of the bowl.
(FULL EXPLANATION)​

Answer 1

Given Parameters :

• Thickness of the hemispherical bowl is 0.25 cm
• Inner radius of the bowl is 5 cm.

Unknown :

• Outer curved surface area of the bowl = ?

Answer :

• The outer curved surface area of the bowl is 173.25 cm ²

Required Explaination :

★ First of all we need to find the outer radius of the hemispherical bowl :

→ Outer radius = Inner radius + thickness of bowl

→ Outer radius = 5 + 0.25

→ Outer radius = 5.25 cm

• Hence,the outer radius of the hemispherical bowl is 5.25 cm.

★ Now, let's find the outer curved surface area of hemispherical bowl :

• Let outer radius of hemispherical bowl be "r".

⇒Outer CSA = 2πr²

⇒Outer CSA = 2 × 22/7 × 5.25 × 5.25

⇒Outer CSA = = 1,212.75 ÷ 7

⇒Outer CSA = 173.25 cm²

• Hence,the outer curved surface area of hemispherical bowl is 173.25 cm².

Answer 2

${\large{\bold{\sf{\bf{\underline{Correct \; question}}}}}}$

➨ A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

${\large{\bold{\sf{\bf{\underline{Given \; that}}}}}}$

➨ Thickness of steel which bowl is made = 0.25 cm

➨ The inner radius of the bowl = 5 cm.

${\large{\bold{\sf{\bf{\underline{To \; find}}}}}}$

➨ The outer curved surface area of the bowl.

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

➨ The outer curved surface area of the bowl = 173.25 cm²

${\large{\bold{\sf{\bf{\underline{Full \; solution}}}}}}$

~ Let us find the outer radius of bowl

➝ Outer radius = Inner radius + Thickness of bowl

➝ Outer radius = 5 + 0.25

➝ Outer radius = 5.25 cm

${\pink{\frak{Henceforth, 5.25 \: cm \: is \: outer \: radius \: of \: bowl}}}$

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~ Let's find the outer curved surface area of the bowl.

➝ Outer CSA = 2πr²

➝ Outer CSA = 2 × 3.14 × 5.25²

➝ Outer CSA = 2 × 3.14 × 5.25 × 5.25

➝ Outer CSA = 2 × 3.14 × 27.5625

➝ Outer CSA = 2 × 86.54625

➝ Outer CSA = 173.25 cm²

${\pink{\frak{Henceforth, 173.25 \: cm^{2} \: is \: outer \: CSA \: of \: bowl}}}$

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${\large{\bold{\sf{\bf{\underbrace{Additional \; knowledge}}}}}}$

Sphere's diagram –

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

Formulas related to circle –

${\large{\pink{\bold{\sf{\bullet \longrightarrow Area \; of \; circle = \pi r^{2}}}}}}$

${\large{\pink{\bold{\sf{\bullet \longrightarrow Circumference \; of \; circle = 2 \times \pi \times r}}}}}$

${\large{\pink{\bold{\sf{\bullet \longrightarrow Diameter \; of \; circle = 2 \times r}}}}}$

${\large{\pink{\bold{\sf{\bullet \longrightarrow Radius \; of \; circle = \dfrac{Diameter}{2}}}}}}$

Formulas related to cylinder -

$\boxed{\begin{minipage}{6.5 cm}\bigstar \:\underbrace{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

Diagram –

Diagram of this question is given in attachment.

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