30. A big candle is made up of a pyramid with a slant height of attached to a cuboid with a square base of sides and a height of . (i) Calculate the volume of the candle. Another candle is made in the shape of a sphere. The volume of this candle is one-tenth the volume of the big candle. (ii) Show that the radius of the spherical candle is , correct to 3 significant figures. The diagram shows the plan view of a box holding two of the spherical candles. The candles just fit into the box in the shape of a cuboid. (iii) Calculate the volume of empty space in the box.30. A big candle is made up of a pyramid with a slant height of attached to a cuboid with a square base of sides and a height of . (i) Calculate the volume of the candle. Another candle is made in the shape of a sphere. The volume of this candle is one-tenth the volume of the big candle. (ii) Show that the radius of the spherical candle is , correct to 3 significant figures. The diagram shows the plan view of a box holding two of the spherical candles. The candles just fit into the box in the shape of a cuboid. (iii) Calculate the volume of empty space in the box.
