Volumes of cylinders and composite objects

Question

a. This cake is made of three cakes, each 15 cm high, and with diameters 20 cm, 30 cm and 40 cm. Calculate the total volume of the cake.

b. How many litres of liquid concrete were used to make this sculpture? First find its volume (1 cm³ = 1 mL; 1 m³ = 1 KL). Give your answer correct to one decimal place.

c. This solid wooden block is a cylinder (diameter 2 m, perpendicular height 3 m) which has had three circular holes drilled through it, each with diameter 30 cm. Calculate the volume of wood remaining. Give your answer correct to two decimal places.

Answer 1

pir^2 for each cake where r= 40/2, 30/2 and 20/2 = 20,15 and 10

pi(20^2)15 + pi(15^2)15 + pi(10^2)15

= 15pi(400+ 225 + 100)

= 15pi(725)

= about 34,164.82 cm^3

Answer 2

Part a has been answered.

For Part b, a diagram is needed

Part c:

Volume of wood remaining = volume of block before drilling - volume removed by drilling

= π(1m)²(3m) - 3[π(0.15m)²(3m)]