Question

radius and slant height of vessel are 35cm and 91cm find capacity​

Answer 1

Answer:

The required capacity of the vessel is 107800 cm³

Step-by-step explanation:

Given :

• Radius of a vessel, r = 35 cm
• Slant height of a vessel, l = 91 cm

To find :

the capacity of the vessel

Solution :

Since radius and slant height are given, let's find the height of the cone.

We know,

   $\underline{\boxed{\bf l=\sqrt{r^2+h^2}}}$

   h² = l² - r²

   h² = 91² - 35²

   h² = 8281 - 1225

   h² = 7056

   h = √7056

   h = 84 cm

Volume of a cone is given by,

 $\boxed{\tt V=\dfrac{1}{3} \pi r^2h}$

$\longrightarrow \sf V=\dfrac{1}{3} \times \dfrac{22}{7} \times 35 \times 35 \times 84 \ cm^3 \\\\ \longrightarrow \sf V=22 \times 5 \times 35 \times 28 cm^3 \\\\ \longrightarrow \sf V=107800 \ cm^3$

Hence, the capacity of the vessel is 107800 cm³ (or) 0.1078 m³

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Know more :

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+l)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$