Question

the diameter of a solid hemisphere is 42cm. find its volume,curved surface area and total surface area.

Answer 1

diameter ka half krke sb formule ka value rakh do

Answer 2

Solution :

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Given :

The diameter of a solid hemisphere is 42cm,.

⇒ Shape & Dimension given : Hemi - sphere,.

⇒ d = 42cm

We know that,

⇒ d = 2r (diameter is twice the radius)

So,

⇒ 2r = 42

⇒ r = $\frac{42}{2}$

⇒ ∴ r = 21cm,.

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To find :

The Volume, CSA & TSA, of the given shape (Hemi - sphere)

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We know that,

Volume of Hemi - sphere = $\frac{2}{3} \pi r^3$

⇒ $\frac{2}{3}( \frac{22}{7} ) (42)(42)(42)$

⇒ $\frac{2}{3}( \frac{22}{7} ) (6)(7)(42)(42)$

⇒ $\frac{2}{3}( {22} ) (6)(42)(42)$

⇒ $\frac{2}{3}({22}) (2)(3)(42)(42)$

⇒ $\frac{2}{3}( 22) (2)(42)(42)$

⇒ $({2})(22) (2)(42)(42)$

⇒ (44)(1,764)(2)

⇒ (44)(3,528)

⇒ 1,55,232 cm³

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We know that,

TSA of Hemi - sphere = $3 \pi r^2$

⇒ $3( \frac{22}{7} )(42)(42)$

⇒ $(3)( \frac{22}{7}) (7)(6)(42)$

⇒ $3(22)(6)(42)$

⇒ $(66)(6)(42)$

⇒ (396)(42)

⇒ 16,632 cm²

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CSA of Hemi-sphere : $2 \pi r^2$

⇒ $2( \frac{22}{7} )(42)(42)$

⇒ $2 ( \frac{22}{7} )(6)(7)(42)$

⇒ $2(22)(6)(42)$

⇒ $(44)(6)(42)$

⇒ (264)(42)

⇒ 11088 cm³

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