Question

a solid is in the form of a right circular cylinder with a hemisphere shape at one end and a cone at the other end. their common diameter is 4.2 cm and heights of the cylindrical and conical portion are 12 cm and 7cm. respectively find the volume of the solid toy (π = 22/7)​

Answer 1

•SOLUTION:-

$\bf •The \: shape \: of \: the \: toy \: is \: attached \: above⇭$

$\bf➢ Radius \: of \: the \: hemisphere =2.1cm$

$\bf \: ➢ Radius \: of \: cylinder =2.1cm$

$\bf ➢Radius \: of \: the \: base \: of \: the \: cone =2.1 cm$

$\bf➢Height \: of \: the \: cylinder(H)=12cm$

$\bf➢Height \: of \: the \: cone(h)=7cm$

⇨Volume of the given toy =(volume of the hemisphere + volume of the cylinder + volume of the cone)

$\bf•Volume \: of \: hemisphere = \frac{2}{3} \pi r³$

$\bf•Volume \: of \: cylinder= \pi r²H$

$\bf • Volume \: of \: cone= \frac{1}{3} \pi r²h$

$\bf➦Now ,Volume \: of \: the \: toy=$

$\bf \: \: \: \: \: \: \: \: \: \: = \huge( \small \frac{2}{3} \pi r {}^{3} + \pi r {}^{2} H+ \frac{1}{3} \pi r²h \huge) \small cm {}^{3}$

$\: \: \: \: \: \: \: \: \: \: \bf = \huge[ \small \frac{2}{3} \pi×(2.1)³+ \pi×(2.1)²w×12+ \frac{1}{3} \pi×(2.1)² \huge] \small cm³$

$\: \: \: \: \: \: \: \: \: \: \bf = \frac{1}{3} \pi \times (2.1) {}^{2} \big [ \small2×(2.1)+3×12+7 \big ] \small \: cm {}^{3}$

$\: \: \: \: \: \: \: \: \: \: \bf = \huge[ \small \frac{1}{3} \pi×(2.1)²×47.2 \huge] \small \: cm³$

$\: \: \: \: \: \: \: \: \: \: = \bf \huge( \small \frac{1}{ \cancel{3}} × \frac{22}{ \cancel{7}} × \frac{ {\cancel{21 }\: \:\cancel{3 }}}{10} \times \frac{21}{10} \times \frac{472}{10} \huge) \small \: cm {}^{3}$

$\bf \: \: \: \: \: \: \: \: \: \: = 218.064 \: cm {}^{3}$

➠Hence,the volume of the given toy is 218.064 cm³

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Answer 2

Answer:

FIGURE IS IN THE ATTACHMENT.

SOLUTION:

GIVEN:

Height of the conical portion (h1)= 7 cm

height of the cylindrical portion (h2)= 12 cm

Diameter of Cylinder, cone & hemisphere= 4.2 cm

Radius of Cylinder, cone & hemisphere(r)= Diameter/2 = 4.2/2 = 2.1 cm

Volume of the solid toy = Volume of the conical portion + Volume of the cylindrical portion + Volume of the hemispherical portion

Volume of the solid toy = 1/3πr²h1 + πr²h2 + 2/3πr³

Volume of the solid toy = 1/3πr²[h1 + 3×h2 +2r ]

Volume of the solid toy =1/3×π ×(2.1)² [7 +3×12 + 2× 2.1]

= 1/3×π ×( 2.1)² [7 + 36 + 4.2]

= 1/3×π×( 2.1)²[43+ 4.2]

= 1/3×π×( 2.1)²[47.2]

= (⅓) × (22/7) × 2.1 × 2.1 × 47.2

= 22 × 0.7 × 0.3 × 47.2

= 218.064 cm³

Hence, the volume of the solid toy = 218.064 cm³.

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