the dimensions of two rectangular prisms with volume 240 cm^3 are given. sketch each prism and predict which will have less surface area. check your prediction.
a) 10cm by 6cm by 4cm
b) 12cm by 10 cm by 2cm
correct
my answer:
A) SA= 2((6*10)+(4*10)+(4*6))
SA=2(124)
SA=248cm^2
B) SA= 2((10*12)+(2*12)+(2*10))
SA=2(164)
SA=328cm^2
is my answer correct?
To predict which prism will have less surface area, we need to calculate the surface area of each prism. The formula for the surface area of a rectangular prism is given by:
Surface Area = 2(length × width + length × height + width × height)
Let's calculate the surface area of each prism:
a) Prism with dimensions 10cm by 6cm by 4cm:
Surface Area = 2(10cm × 6cm + 10cm × 4cm + 6cm × 4cm)
Surface Area = 2(60cm² + 40cm² + 24cm²)
Surface Area = 2(124cm²)
Surface Area = 248cm²
b) Prism with dimensions 12cm by 10cm by 2cm:
Surface Area = 2(12cm × 10cm + 12cm × 2cm + 10cm × 2cm)
Surface Area = 2(120cm² + 24cm² + 20cm²)
Surface Area = 2(164cm²)
Surface Area = 328cm²
From the calculations, we can see that the prism with dimensions 10cm by 6cm by 4cm (Prism "a") has a surface area of 248cm², while the prism with dimensions 12cm by 10cm by 2cm (Prism "b") has a surface area of 328cm².
Therefore, Prism "a" will have less surface area compared to Prism "b".