Answers
Set 68
- c.When the faces of a rectangular prism are laid side-by-side, you
always have three pairs of congruent faces. That means every face
of the prism (and there are six faces) has one other face that shares
its shape, size, and area. - b.The original cube has a side length of x, so after it is tripled, the
side length will by 3x. A cube with a side length of 3xwill have six
faces that each have an area of 9x^2. Therefore the surface area will
be 6(9x^2 ) cm^2 = 72x^2 cm^2. (Although it is tempting to just triple 6x^2
cm2 to 18x^2 cm^2 , that will not work because it does not take into
consideration that eachside length has tripled.)
Set 69
- Surface Area= 260.24 square inches.Begin by finding the whole
surface area: surface area = (SA= 2[(17)(5.2) + (5.2)(3.7) + (17.6)(3.7)
= 351.76 in^2 .) From the total surface area, subtract the area of the
missing face: Remaining SA = 351.76 sq. in. – 91.52 sq. in.
Remaining SA = 260.24 square inches. - c. The surface area of Marvin’s gift is 6d^2. Although it is tempting
to just double 6d^2 to 12d^2 , that will not work because it doesn’t
take into consideration that eachside length has doubled. Instead
you must consider Maya’s gift that has an edge length of 2d, which
will in turn have 6 faces that are each 4d^2 in area. The total surface
area of Maya’s gift will be 6 × 4 d^2 = 24d^2. - Surface Area= 318 feet^2 .These next few problems are tricky:
Carefully look at the diagram. Notice that the top of each cubed
leg is not an exposed surface area, nor is the space they occupy
under the large rectangular prism. Let’s find these surface areas
first. The top of each cubed leg equals the square of the length of
the cube: (2 feet) = 4 sq. ft. There are four congruent cubes, four
congruent faces: 4 ×4 sq. ft. = 16 sq. ft. It is reasonable to assume
that where the cubes meet the rectangular prism, an equal amount
501 Geometry Questions