The shadow portion in the figure is made of cutting off four isosceles triangles 2cm in height from the square which is 8 cm one side.
Find the volume of the quadrangular pyramid made by assembling this development.
Find the volume of the quadrangular pyramid made by assembling this development.
Answer
When the solid of Fig. 1 is equally divided into four, one solid will become triangular pyramid A-BCD of Fig. 3.
The development view of triangular pyramid A-BCD becomes the square which divided the development view in the problem into four equally as shown in Fig. 2.
The height of the solid of Fig. 1 is equal to the length of one side of the small square of Fig. 2.
It is 8cm / 2 = 4cm.
The area of a square at the bottom is 4cm × 4cm / 2 = 8cm2.
The volume of the solid is 8cm2 × 4cm × 1/3 = 32/3cm3.
32/3 cm3
Solution
Fig. 1 is a sketch of the solid which assembled the portion of the shadow.
When the solid of Fig. 1 is equally divided into four, one solid will become triangular pyramid A-BCD of Fig. 3.
The development view of triangular pyramid A-BCD becomes the square which divided the development view in the problem into four equally as shown in Fig. 2.
The height of the solid of Fig. 1 is equal to the length of one side of the small square of Fig. 2.
It is 8cm / 2 = 4cm.
The area of a square at the bottom is 4cm × 4cm / 2 = 8cm2.
The volume of the solid is 8cm2 × 4cm × 1/3 = 32/3cm3.
