Question

a cone of height 15cms and diameter 7ms is mounted on a hemisphere of same diameter. determine the volume of solid thus formed and also tsa of solid formed(explain with neat diagram)

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Answer 1

$\tt\red{Height \;of\;\;the\;cone=15\;cm}$

$\tt\red{Diameter \;of\;the\;cone=7\;cm}$

$\tt\red{So, \; it's\; radius\;=3.5\;cm}$

$\tt\red{Radius\; of\; the \;hemisphere=3.5\;cm}$

$\tt\red{Now,}$

$\small\tt\red{Volume \;of\; Solid=\; Volume\;of\;the\;cone\;+Volume\;of\;the\; hemisphere}$

$\tt\red{\implies \frac{1}{3} \pi {r}^{2}h + \frac{2}{3} \pi {r}∗{3}}$

$\tt \red{ \implies \frac{1}{3} \times \frac{22}{7} \times (3.5) ^{2} \times 15 + \frac{2}{3} \times \frac{22}{7} \times (3.5) ^{3} }$

$\tt \red{ \implies \frac{1}{3} \times \frac{22}{7} \times (3.5) ^{2} (15 + 2 \times 3.5)}$

$\tt \red{ \implies \frac{827}{3} }$

$\bf \green{ \implies282.33 \: {cm}^{3} }$

Answer 2

$\huge\color{red}{\mid{\fbox{\tt{αηsωεя}}\mid}}$

Height of the cone=15cm

Diameter of the cone=7cm

So,it

sradius=3.5cm

Radius of the hemisphere =3.5cm

Now,

Volume of Solid=Volume of the cone+Volume of the hemisphere.

⟹ 1/3 πr²h + 2/3πr×3

⟹ 1/3 × 7/22 ×(3.5)² × 15 + 2/3 × 2/7 × (3.5)³

⟹ 1/3 × 7/22 ×(3.5)² × 15 + 2× 3.5³

⟹ 382/7

⟹ 282.33cm