Question

Determine the volume of a conical tin having radius of the base as 30 cm and its slant height as 50 cm. Find its Total surface area also.​

Answer 1

Answer:

Volume of the conical tin is 6280 cubic cm.

Step-by-step explanation:

Formula used:

1.Volume of cone=\frac{1}{3}\:\pi\:r^2h=

3

1

πr

2

h cubic units

2.l^2=h^2+r^22.l

2

=h

2

+r

2

Let r, h and l be radius, height and slant height of the conical tin respectively.

Given:

Radius of the conical tin, r = 30 cm

Slant height of the conical tin, l=50 cm

\begin{gathered}l^2=h^2+r^2\\\\(50)^2=h^2+(30)^2\\\\2500=h^2+900\\\\h^2=2500-900\\\\h^2=1600\\\\h=\sqrt{1600}\\\\h=40\:cm\end{gathered}

l

2

=h

2

+r

2

(50)

2

=h

2

+(30)

2

2500=h

2

+900

h

2

=2500−900

h

2

=1600

h=

1600

h=40cm

Now,

Volume of the conical tin

\begin{gathered}=\frac{1}{3}\:\pi\:r^2h\\\\=\frac{1}{3}\:(3.14)\:(30)^2(40)\\\\=\frac{1}{3}\:(3.14)\:(30)^2(40)\\\\=\frac{1}{3}\:(3.14)\:(900)(40)\\\\=3.14*300*40\\\\=314*3*40\\\\=314*120\\\\=6280 \;cubic \:cm.\end{gathered}

=

3

1

πr

2

h

=

3

1

(3.14)(30)

2

(40)

=

3

1

(3.14)(30)

2

(40)

=

3

1

(3.14)(900)(40)

=3.14∗300∗40

=314∗3∗40

=314∗120

=6280cubiccm.

Answer 2

Required Answer:

• Radius of the base (r) = 30cm
• Slanted height (l) = 50cm

We can Find its perpendicular height by using Pythagoras theorem;

(H)² = (B)² + (P)²

Where as:

• H = Hypotenuse (Slanted height)
• B = Base
• P = Perpendicular height

After substituting the values;

➦ (50)² = (30)² + (p)²

➦ 2500 = 900 + p²

➦ 2500 - 900 = p²

➦ 1600 = p²

➦ P = 40 cm (Perpendicular height)

___________________________

• ${\boxed{\sf\red{ Volume_{(cone)} = \dfrac{1}{3} πr^2 h }}}$

Where as;

• r = Radius of base
• h = perpendicular height

After putting values;

➦ ⅓ × 22/7 × 30 × 30 × 40

➦ 37680 cm³

___________________________

• ${\boxed{\sf\red{ Total\: surface \: area_{(cone)} = πrl + πr^2 }}}$

Where as;

• l = slanted height
• r = Radius of base

After putting values;

➦ 22/7 × 30 × 50 + 22/7 × 30 × 30

➦ 4710 + 2826

➦ 7536 cm²