Volumes Practice Test 4

Let radius and height of a right circular cone are 5x cm and 12x cm.
Then, $\frac{1}{3}\times 3.14\times {\left(5\mathit{x}\right)}^2\times 12\mathit{x}$ = 2512
⇒ ${\mathit{x}}^3$ = $\frac{2512}{3.14\times 25\times 4}$ = 8
∴ x = 2
Since, radius = 5 × 2 = 10 cm; height = 12 × 2 = 24 cm
Now, slant height, l = $\sqrt{{10}^2+{24}^2}$ = $\sqrt{676}$ = 26 cm
Curved surface area = 3.14 × 10 × 26 = 816.4 $\mathit{c}{\mathit{m}}^2$
Total surface area = 3.14 × 10 × 26 + 3.14 × (10)2 = 816.4 + 314 = 1130.4 $\mathit{c}{\mathit{m}}^2$