Question

The base radius of a solid right circular iron rod is 32 cm. and its length is 35 cm. Let us
calculate the number of solid cones of 8 cm. radius and 28 cm. height can be made by
melting this rod.
made from soli?​

Answer 1

✬ Cones = 60 ✬

Step-by-step explanation:

Given:

• An iron rod is in shape of right circular cylinder.
• Base radius of cylinder is 32 cm.
• Length of cylinder is 35 cm.
• Rod is reshaped into solid cones of 8 cm radius and 28 cm height.

To Find:

• How many cones are made ?

Solution: Since rod is recasted into cones therefore,

➟ Volume of cylinder = Volume of cone

As we know that

★ Volume of Cylinder = πr²h ★

★ Volume of cone = 1/3πr³ ★

$\implies{\rm }$ Cylinder = π × 32² × 35

$\implies{\rm }$ π × 1024 × 35

$\implies{\rm }$ 35840π........i

Similarly

$\implies{\rm }$ Cone = 1/3π × 8² × 28

$\implies{\rm }$ π/3 × 64 × 28

$\implies{\rm }$ 1792π/3.......ii

➮ 35840π = 1792π/3

➮ 35840 × 3 = 1792

➮ 107520/1792

➮ 60 cones

Hence, 60 solid cones can be made from by melting iron rod.

Answer 2

Given :

• The base radius of a solid right circular iron rod is 32 cm. and its length is 35 cm

• the number of solid cones of 8 cm. radius and 28 cm.

To Find :

• height can be made by melting this rod. made from soli?

Solution :

Let the number of solids :

$\sf : \implies \: \: \: \: \: \: \: \: \frac{1}{3} \: \pi {r}^{2} h \times n = \pi {R}^{2} H \:$

Substitute all values :

$\sf : \implies \: \: \: \: \: \: \: \: \frac{1}{3} \: \pi \times {8}^{2} \times 28\times n = \pi \times {32}^{2} \times 35 \: \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \frac{1}{3} \: 64 \times 28 \times n = 32 \times 32 \times 35 \\ \\ \\ \sf : \implies \: \: \: \: \: \: \:n = \frac{ \cancel{32 }\times 32 \times 35\times 3}{\:\cancel{64} \times 28} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \:n = \: \frac{ \cancel{32} \times 35\times 3}{2 \times \cancel{ 28} } \\ \\ \\ \sf : \implies \: \: \: \: \: \: \:n = \cancel{\frac{280\times 3 }{14}} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \:n = 60$