Final answer:
The surface area of a rectangular pyramid with a height of 9 centimeters and a base with dimensions of 5 centimeters by 6 centimeters is 234 cm².
Step-by-step explanation:
To determine which statements are true about a rectangular pyramid with a height of 9 centimeters and a base with dimensions of 5 centimeters by 6 centimeters, we can calculate the volume, surface area, slant height, and lateral area.
A. The volume is 270 cm³.
To calculate the volume, we use the formula V = (1/3) × base area × height. The base area is 5 cm × 6 cm = 30 cm². Substitute the values into the formula: V = (1/3) × 30 cm² × 9 cm = 90 cm³, not 270 cm³.
C. The slant height is 10.63 cm.
To find the slant height, we can use the Pythagorean theorem. The slant height, height, and half the base form a right triangle. Using a² + b² = c², we have (5/2)² + 9² = c². Simplifying, we get 6.25 + 81 = c², which gives us c = √87.25 ≈ 9.35 cm, not 10.63 cm.
D. The lateral area is 90 cm².
To find the lateral area, we sum the areas of the four triangular faces. Each triangular face has a base of either 5 cm or 6 cm and a height of 9 cm. Therefore, the lateral area is (5 cm × 9 cm) + (5 cm × 9 cm) + (6 cm × 9 cm) + (6 cm × 9 cm) = 270 cm², not 90 cm².
Therefore, B. The surface area is 234 cm² is the only true statement.