Question 15
A four-layer tower is built from 30 unit cubes of side 1 cm as shown. The top layer contains 1 cube, the second 4, the third 9 and the bottom 16. All exterior faces, including the bottom, are painted.
(1) Find the area of each face of a unit cube.
(2) What shape do we see when looking at the tower directly from above? Find the visible area from above.
(3) What shape do we see when looking at the tower from below? Find the visible area from below.
(4) What shape do we see when looking at the tower from its four sides? Find the area visible from all four sides.
(5) What is the total painted area of the tower?
(1) Find the area of each face of a unit cube.
(2) What shape do we see when looking at the tower directly from above? Find the visible area from above.
(3) What shape do we see when looking at the tower from below? Find the visible area from below.
(4) What shape do we see when looking at the tower from its four sides? Find the area visible from all four sides.
(5) What is the total painted area of the tower?