-
The base of a right pyramid is an equilateral triangle of side 10√3 cm. If the total surface area of the pyramid is 270√3 sq. cm, its height is
-
- 12√3cm
- 10 cm
- 10√3cm
- 12 cm
- 12√3cm
Correct Option: D
AB = 10√3 cm
BE = 5√3 cm
AE = √(10√3)² - (5√3)²
= √225 = 15 cm
| OE = | × 15 = 5 cm. | |
| 3 |
Let the height of pyramid be h cm, then
Slant height = √h² + 5² = √h² + 25
Now, Total surface area = Area of the 3 faces + Area of base
| = 3 |  | base × slantheight |  | + Area of the base | |
| 2 |
| Total surface area = | × (perimeter of base) × (slant height) + Area of base [base of all the 3 triangular faces is the edge of the equilateral triangle]. | |
| 2 |
| ⇒ 270√3 - | × 30√3 × √h² + 25 + | × (10√3)² | ||
| 2 | 4 |
⇒ 270√3 - 15√3√h² + 25 + 75√3
⇒ 15√3√h² + 25 = 195√3
⇒√h² + 25 = 13
⇒ h² + 25 = 169
⇒ h² = 169 – 25 = 144
⇒ h = 144 = 12 cm
