1) A mooncake is in cylindrical form of radius 4cm and height 3cm. Some mooncakes of this size are packed into a closed rectangular box measuring 40cm by 16cm by 6cm.
a) Calculate the volume of one mooncake.
b) At most how many such mooncakes can be packed into the box?
c) When the box is filled with mooncakes, find the volume of the empty space in the box.
d) If the mooncakes are to be wrapped individually, how many wrapping materials are needed?
e) Can a new box measuring 32cm by 10cm by 12 cm hold as many mooncakes as the original box?
2) A solid consists of a cone, a cylinder and a hemisphere. The base radius is 4cm. the ratio of the volumes of the cone, cylinder and the hemisphere is 6:27:4. Find:
a) the height of the cone,
b) the height of the cylinder,
c) the volume of the solid,
d) the surface area of the solid.
a) Calculate the volume of one mooncake.
b) At most how many such mooncakes can be packed into the box?
c) When the box is filled with mooncakes, find the volume of the empty space in the box.
d) If the mooncakes are to be wrapped individually, how many wrapping materials are needed?
e) Can a new box measuring 32cm by 10cm by 12 cm hold as many mooncakes as the original box?
2) A solid consists of a cone, a cylinder and a hemisphere. The base radius is 4cm. the ratio of the volumes of the cone, cylinder and the hemisphere is 6:27:4. Find:
a) the height of the cone,
b) the height of the cylinder,
c) the volume of the solid,
d) the surface area of the solid.