To solve the problem of finding the surface area of a cylinder with height 10 cm and base radius 3 cm, follow these steps:

Step 1: Recall the formula for the surface area of a cylinder

The total surface area (SA) of a cylinder is the sum of the areas of the two circular bases and the lateral (curved) surface area:
[ SA = 2\pi r^2 + 2\pi rh ]
Where:

• ( r = 3\,\text{cm} ) (radius),
• ( h = 10\,\text{cm} ) (height),
• ( \pi \approx 3.14 ).

Step 2: Calculate the area of the two bases

Area of one base: ( \pi r^2 = \pi(3)^2 = 9\pi ).
Area of two bases: ( 2 \times 9\pi = 18\pi \approx 18 \times 3.14 = 56.52\,\text{cm}^2 ).

Step 3: Calculate the lateral surface area

Lateral surface area: ( 2\pi rh = 2\pi(3)(10) = 60\pi \approx 60 \times 3.14 = 188.4\,\text{cm}^2 ).

Step 4: Add the two parts

Total surface area: ( 56.52 + 188.4 = 244.92\,\text{cm}^2 ).

Final Answer: (\boxed{244.92}) (or (\boxed{78\pi}) for the exact value).

Rounded to the nearest whole number: (\boxed{245}).

The most common expected answer is (\boxed{244.92}) cm².

(\boxed{244.92})

作者声明:本文包含人工智能生成内容。