A hemispherical bowl of radius $10$ cm stands with its flat rim on top, as in the picture. It holds water $4$ cm deep at the middle. What volume of water does it hold?

Fig. 1: The cross-section of a hemispherical bowl of radius 10 cm, drawn as a half circle with a flat top. A grey arrow of length 10 cm runs from the centre of the flat top to the curved wall. A red horizontal line near the bottom marks the water surface, and the water below it is shaded light blue. A double arrow at the right marks the depth of the water as 4 cm.