A cylindrical mould of iron of radius 6 cm is used to make 2 conical shape ice-creams of radius 2 cm-each:If height of ice-cream is 60% of height of mould then find volume of the mould if height of mould is 5 time the radius of ice-cream.

Options

A. 340 7 `pi cm^(3)`
B. 352 `pi cm^(3)`
C. 342 `pi cm^(3)`
D. 344 `pi cm^(3)`

Answer

To solve the problem step by step, we will calculate the volume of the cylindrical mould and then find the volume of the two conical ice creams to subtract from the mould's volume.

### Step 1: Identify the radius and height of the cylindrical mould.
- Given radius of the mould \( R = 6 \) cm.
- Height of the mould \( H \) is given as 5 times the radius of the ice-cream.

### Step 2: Calculate the radius of the ice-cream.
- Given radius of the ice-cream \( r = 2 \) cm.

### Step 3: Calculate the height of the mould.
- Height of the mould \( H = 5 \times r = 5 \times 2 = 10 \) cm.

### Step 4: Calculate the height of the ice-cream.
- The height of the ice-cream is 60% of the height of the mould.
- Height of the ice-cream \( h = 60\% \times H = 0.6 \times 10 = 6 \) cm.

### Step 5: Calculate the volume of the cylindrical mould.
- The formula for the volume of a cylinder is given by:
\[ V_{\text{cylinder}} = \pi R^2 H \]
- Substituting the values:
\[ V_{\text{cylinder}} = \pi (6^2)(10) = \pi (36)(10) = 360\pi \text{ cm}^3 \]

### Step 6: Calculate the volume of one conical ice-cream.
- The formula for the volume of a cone is given by:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
- Substituting the values for one cone:
\[ V_{\text{cone}} = \frac{1}{3} \pi (2^2)(6) = \frac{1}{3} \pi (4)(6) = \frac{24}{3} \pi = 8\pi \text{ cm}^3 \]

### Step 7: Calculate the volume of two conical ice-creams.
- Since there are two ice-creams:
\[ V_{\text{total cones}} = 2 \times V_{\text{cone}} = 2 \times 8\pi = 16\pi \text{ cm}^3 \]

### Step 8: Calculate the remaining volume in the mould after making the ice-creams.
- Remaining volume in the mould:
\[ V_{\text{remaining}} = V_{\text{cylinder}} - V_{\text{total cones}} = 360\pi - 16\pi = 344\pi \text{ cm}^3 \]

### Final Answer
- The volume of the mould after making the ice-creams is \( 344\pi \text{ cm}^3 \).

---