Question

The volume of Pyramid A is 704 cm3 and the volume of Pyramid B is 297 cm3. If the pyramids are similar and the surface area of Pyramid B is 153 cm2, what is the the surface area of Pyramid A?

Answer 1

Answer:

272 cm²

Step-by-step explanation:

Step 1

We have to find the scale factor

When given the volume of two solids, the formula for the scale factor is

V1/V2 = (Scale factor)³

The volume of Pyramid A is 704 cm³ and the volume of Pyramid B is 297 cm³

V1 = Pyramid A

V2 = Pyramid B

704/297 = (scale factor)³

We simplify the left hand side to simplest fraction

The greatest common factor of 704 and 297 = 11

704÷11/297÷11 = (scale factor)³

64/27 = (scale factor)³

We cube root both sides

cube root(scale factor)³ = cube root (64/27)

scale factor = (4/3)

Step 2

(Scale factor)² = S1/S2

S1 = Surface area of Pyramid A =?

S2 = Surface area of Pyramid B = 153 cm²

Hence,

(4/3)² = S1/153

16/9 = S1/153

Cross Multiply

S1 × 9 = 16 × 153

S1 = 16 × 153/9

S1 = 272 cm²

Therefore, the Surface Area of Pyramid A = 272 cm²