SOLUTION: The base of the solid figure shown is a cube with sides that measure 6 inches. The top portion is a square pyramid with a slant height of 5 inches. The total height of the figure i

Question 1011569: The base of the solid figure shown is a cube with sides that measure 6 inches. The top portion is a square pyramid with a slant height of 5 inches. The total height of the figure is 10 inches. What is the total surface area of the solid?
a)240
b)264
c)276
d)300

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52833)   (Show Source): You can put this solution on YOUR website!
.
The base of the solid figure shown is a cube with sides that measure 6 inches. The top portion is a square pyramid
with a slant height of 5 inches. The total height of the figure is 10 inches. What is the total surface area of the solid?
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The surface area of the lower portion of the solid consists of the surface areas of 5 squares 6x6 inches each, so it is 5*6*6 = 180 square inches. The top portion surface area consists of four triangles with the base 6 inches anf the height of 5 inches (slant height). So, the top portion surface area is 4*.6*5 = 60 square inches. The total surface area is 180 + 60 square inches, which is 240 square inches. Answer is a).

Notice. One condition is excessive.

Taking into account that the base is the cube with the side 6 inches, these two phrases
    "The top portion is a square pyramid with a slant height of 5 inches".   and
    "The total height of the figure is 10 inches"
carry the same information.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
The base of the solid figure shown is a cube with sides that measure inches.
the total surface area of the base is:

The top portion is a square pyramid with a slant height of
the total surface area of the square pyramid without base (base area is already included in cube area) will be:

then, the total surface area of the solid is
so, your answer is: c.

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