A cone of maximum volume is carved out of a block of wood of size 20 cm × 10 cm × 10 cm. Find the volume of the cone carved out, correct to one decimal place.

Volume of block of wood = 20 cm × 10 cm × 10 cm = 2000 cm³

Diameter of the cone for maximum volume = 10 cm

Cone of maximum volume is carved out as shown in figure,

Radius, r = $\dfrac{\text{diameter}}{2} = \dfrac{10}{2}$ = 5 cm.

Height of the cone for maximum volume, h = 20 cm

Volume of cone = $\dfrac{1}{3}$ πr²h

$= \dfrac{1}{3} \times \dfrac{22}{7} \times 5^2 \times 20 \\[1em] = \dfrac{1}{3} \times \dfrac{22}{7} \times 25 \times 20 \\[1em] = \dfrac{11000}{21} \\[1em] = 523.8 \text{ cm}^3.$

Hence, the volume of the cone carved out is 523.8 cm³.