Question

Determine the volume of a conical tin having radius of the base as 30cm and its slant height as 50cm (useπ=3.14)

Answer 1

Answer:

Volume of the conical tin is 6280 cubic cm.

Step-by-step explanation:

Formula used:

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

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

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

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

Now,

Volume of the conical tin

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

Answer 2

Step-by-step explanation:

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.