A playing top (lattu) is shaped like a cone surmounted by a hemisphere. The total height is 5 cm and the diameter is 3.5 cm. Find the surface area to be coloured.

Step 1: Identify Dimensions

First, we need to determine the radius of the hemisphere and the cone, which is half of the given diameter. Then, we can find the height of the conical part by subtracting the radius of the hemisphere from the total height of the top.

Step 2: Calculate Slant Height of Cone

To find the curved surface area of the cone, we need its slant height ($l$). We can calculate this using the Pythagorean theorem, where $r$ is the radius and $h$ is the height of the cone.

Step 3: Calculate Curved Surface Area of Hemisphere

The surface area to be colored includes the curved surface area of the hemispherical part. The formula for the curved surface area of a hemisphere is $2\pi r^2$, where $r$ is the radius.

Step 4: Calculate Curved Surface Area of Cone

Next, we calculate the curved surface area of the conical part of the top. The formula for the curved surface area of a cone is $\pi r l$, where $r$ is the radius and $l$ is the slant height.

Step 5: Calculate Total Surface Area

The total surface area to be colored is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.

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