By Paul Harrison, Royal Correspondent
The Duke and Duchess of Cambridge have taken to the beaches of Sydney - but kept their shoes on.
Accompanied by Australian Prime Minister Tony Abbott, William and Kate watched a surf life-saving demonstration and met with some of the lifeguards taking part.
The Duchess seemed at ease on the sand despite wearing wedges as she started a race between eight youngsters.
At the end the royal couple was presented with a surfboard, but there would be no riding the royal wave.Kate meets some of the lifeguards of Manly Beach, Sydney
Earlier the Duchess delivered her first and only speech during this tour as she and the Duke visited the Bear Cottage children's hospice, which is forging links with the East Anglia's Children's Hospices (EACH), a UK charity of which she is patron.
"I am delighted that Bear Cottage and EACH are planning to be part of a 'community of best practice'," she told those gathered.
"The haven that you have created here is inspirational, and there is so much that you can share with each other as you continue to support and nurture those in your care."Kate meets some of the residents of Bear Cottage
The Duchess then added that her family had enjoyed a warm Australian welcome.
She said: "If I may, I would also like to take this opportunity to thank everyone who has welcomed me and George so incredibly warmly on our first visit.
"To be here together as a family has been very special and we will always remember it with fond and happy memories."
Earlier, during a wool demonstration at the Sydney Royal Easter Show Kate - wearing a dress by Australian designer Zimmerman - poked fun at her husband's bald patch.The Duke and Duchess see some giant pumpkins
The Duchess was handed some alpaca wool, at which point she turned to William, gestured towards his bald patch and suggested he might need it more than her.
At the show, one of Australia's largest annual events attracting 900,000 visitors each year, William and Kate also came face to face with Fred the ram and a giant pumpkin.
At one point Fred appeared to bow to the future king, while Kate just settled for a quick pet.Prince William talks to a resident of Bear Cottage children's hospice
As well as being treated to a sheep shearing demonstration, the royal couple were wowed by displays of giant fruit and veg produce.
Student Mikayla Rendall had been standing in the sun for four hours waiting for the Duke and Duchess.
She said: "Kate apologised for keeping us waiting in the sun and William said they never get this much sun at Buckingham Palace."