Two cones with the same base radius 8,cm and height 15,cm are joined together along their bases. Find the surface area of the shape so formed.(answer to the nearest whole number)

To solve this problem, we will calculate the surface area of the shape formed by joining two identical cones along their bases.

### Step 1: Understand the structure
When two cones are joined along their bases:
- The base area is no longer part of the surface area since it is internal to the structure.
- The surface area consists of the curved surface areas of both cones.

### Step 2: Formula for the curved surface area of a cone
The curved surface area (CSA) of a cone is given by:
CSA = π * r * l
where:
- r = base radius of the cone
- l = slant height of the cone

### Step 3: Calculate the slant height
The slant height \( l \) is found using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]
Here:
- r = 8 cm
- h = 15 cm

\[ l = \sqrt{8^2 + 15^2} \]
\[ l = \sqrt{64 + 225} \]
\[ l = \sqrt{289} = 17 \, \text{cm} \]

### Step 4: Calculate the curved surface area of one cone
Using \( l = 17 \, \text{cm} \) and \( r = 8 \, \text{cm} \):
\[ \text{CSA of one cone} = \pi \cdot r \cdot l \]
\[ \text{CSA of one cone} = \pi \cdot 8 \cdot 17 \]
\[ \text{CSA of one cone} = 136\pi \]

### Step 5: Calculate the total surface area
Since there are two cones:
\[ \text{Total surface area} = 2 \cdot \text{CSA of one cone} \]
\[ \text{Total surface area} = 2 \cdot 136\pi \]
\[ \text{Total surface area} = 272\pi \]

Using \( \pi \approx 3.1416 \):
\[ \text{Total surface area} = 272 \cdot 3.1416 \]
\[ \text{Total surface area} \approx 855.3 \, \text{cm}^2 \]

### Step 6: Round to the nearest whole number
The total surface area is approximately **855 cm²**.

### Final Answer:
The surface area of the shape is **855 cm²**.