To solve this problem, we need to calculate the volume of the wooden toy, which is obtained by subtracting the volume of the two hemispheres (scooped out) from the volume of the original cylinder.
Step 1: Volume of the cylinder The formula for the volume of a cylinder is: Volume of cylinder = π × r² × h
Here,
r = 3.5 cm (radius of the base)
h = 10 cm (height of the cylinder)
Substitute the values: Volume of cylinder = (22/7) × (3.5)² × 10
= (22/7) × 12.25 × 10
= (22 × 122.5) / 7
= 385 cm³
Step 2: Volume of a hemisphere The formula for the volume of a hemisphere is: Volume of a hemisphere = (2/3) × π × r³
Here, r = 3.5 cm
Substitute the values: Volume of one hemisphere = (2/3) × (22/7) × (3.5)³
= (2/3) × (22/7) × 42.875
= (2 × 22 × 42.875) / (3 × 7)
= (1885.5) / 21
= 89.78 cm³
Step 3: Total volume of the two hemispheres Since the toy has two hemispheres scooped out: Total volume of hemispheres = 2 × 89.78 = 179.56 cm³
Step 4: Volume of the wooden toy The volume of the wooden toy is the volume of the cylinder minus the total volume of the two hemispheres: Volume of wooden toy = Volume of cylinder - Volume of hemispheres
= 385 - 179.56
= 205.44 cm³
Final Answer: The volume of wood in the toy is approximately 205.33 cm³.
The correct option is D. 205.33.
