Answer:
A) 5.12mm³
Explanation:
Step 1
Find the volume of the bigger pyramid
This is a triangular based pyramid.
The formula to use is given as Volume of Pyramid =
1/3 × Area of the triangle × Height
Area of the triangle = 1/2 × 3 mm × 4mm = 6mm²
Volume of the large pyramid = 1/3 × 6mm² × 5mm
= 10mm³
We are given the length of the small pyramid as 4mm
We would be using was is known as scale factor to find the volume of the small pyramid
The scale factor k = (Height of the small pyramid)³/ (Height of the Large pyramid)³
k = 4³/5³
k = Volume of small pyramid/ Volume of large pyramid
Volume of small pyramid = X
Volume of large pyramid = 10mm³
Hence,
4³/5³ = X/10
Cross Multiply
= 4³ × 10 = 5³ × X
X = (4³ × 10)/ 5³
X = 5.12mm³