Question

The lengths of the sides of the base of a right square pyramid are 3 feet, and its slant height is 8 feet. If the sides of the base are increased to 9 feet, and the slant height is increased to 24 feet, by what factor is the surface area multiplied? A. 27 B. 9 C. 6 D. 3

Answer 1

Answer:

B. 9

Step-by-step explanation:

The base of a right square pyramid is a square, and we know that the lengths of the square are 3. We can calculate the original area of the base as: 3 * 3 = 9 ft squared.

The slant height is the height of the triangular sides of the pyramid. We know that it's 8 feet, and that the base of the triangle shares a side with the square, so b = 3. Knowing that h = 8 and b = 3, we can apply the triangle area formula: (b * h) / 2 = (8 * 3) / 2 = 24/2 = 12 ft squared. However, there are 4 triangles, so we multiply 12 by 4: 12 * 4 = 48 ft squared.

We add 48 to 9 to get the total original surface area: 48 + 9 = 57 ft squared.

Now, however, the sides of the base of the square are increased to 9 ft, so our new area is 9 * 9 = 81 ft squared.

The slant height becomes 24 ft, so our new triangle area is: (24 * 9)/2 = 216/2 = 108 ft squared. We multiply that by 4: 108 * 4 = 432 ft squared.

The new surface area is thus 81 + 432 = 513 ft squared.

To find the factor the original surface area is multiplied by, we divide 513 by 57: 513 / 57 = 9.

Thus, the answer is B, 9.

Hope this helps!