Answer:
Step-by-step explanation:
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
The surface area of the Pyramid is 362.67 sq.cm.
The volume of a Rectangular Pyramid is given by
(length * width * height ) / 3
Volume of a pyramid A is 704 cu.cm
Volume of pyramid B is 297 cu.cm.
The pyramids are similar and so their sides will be in proportion.
As the sides are in proportion, the volume of the pyramids will also be in proportion.
Surface Area of Pyramid B is 153 sq.cm
Let Surface Area of Pyramid A is x sq.cm.
Then, 704 : 297 = x : 153
704/ 297 = x / 153
704 * 153 / 297 = x
x = 362.67 sq.cm
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