Question

19.Find the capacity in litres of a conical vessel having height 8 cm and slant height 10

Answer 1

Given :-

▪ A conical vessel having height 8 cm and slant height 10 cm.

To Find :-

▪ Capacity of the vessel

Solution :-

Capacity is referred to as Volume here, So we have to find the volume of the conical vessel in litres. But for finding the volume we need height, radius.

But we are given slant height and height, So let us find the radius of the vessel using the following formula :-

⇒ Slant height = √( Height² + Radius² )

⇒ 10 = √( 8² + r² )

Square both sides,

⇒ 100 = 64 + r²

⇒ 100 - 64 = r²

⇒ r² = 36

⇒ r = 6 cm [ Length can't be negative ]

Now, Let us find the volume

⇒ Volume of Vessel = 1/3 × πr²h

⇒ V = 1/3 × 22/7 × 6² × 8

⇒ V = 22 × 36 × 7 / 21

⇒ V = 5544 / 21

⇒ V = 264 cm³

We know, 1 m³ = 0.001 litre , So

⇒ Capacity = 264 × 0.001

⇒ Capacity = 0.264 litre

Hence, The capacity of the conical vessel is 0.274 litre.

Answer 2

$\huge\tt\underline{Solution}$

$\tt{Height \: of \: conical \: vessel= 8 cm}</p><p>$

$\tt{Slant \: height \: of \: conical \: vessel \:} \\ \tt{ (l) = 10 cm}$

$\tt {r2 + h2 = l2}$

 

$\tt{r2 + 82 = 102}$

$\tt{r2 = 100 - 64 = 36}$

$\tt{r = \sqrt{36}}$

$\tt{r = 6}$

$\tt{Now, volume \: of \: conical \: vessel} \tt \\ { = \frac{1}{3}\pi \: r \: 2h = \frac{1}{3} \times \frac{22}{7} \times 6 \times 6 \times 8 }</p><p></p><p>$

$\tt{301.71} {cm}^{3} = 0.30171 \: liter$

$\tt \huge\boxed {0.30171}$