Answer:
992.43 cm²
Step-by-step explanation:
From the question given above, the following data were obtained:
Volume of shape X (Vₓ) = 130 cm³
Surface area of shape X (SAₓ) = 202 cm²
Volume of shape Y (Vᵧ) = 638.69 cm³
Surface area of shape Y (SAᵧ) =?
The surface area of shape Y can be obtained as follow:
Since the shape are similar, then:
Vₓ / Vᵧ = SAₓ / SAᵧ
130 / 638.69 = 202 / SAᵧ
Cross multiply
130 × SAᵧ = 638.69 × 202
130 × SAᵧ = 129015.38
Divide both side by 130
SAᵧ = 129015.38 / 130
SAᵧ = 992.43 cm²
Thus, surface area of shape Y is 992.43 cm²