If H, C and V are respectively the height, curved surface area and volume of a cone, then what is 3\pi VH^{3}+9V^{2} equal to?

  1. A. C^{2}H^{2} ✓
  2. B. 2C^{2}H^{2}
  3. C. 5C^{2}H^{2}
  4. D. 7C^{2}H^{2}

Correct Answer: A. C^{2}H^{2}

Explanation

For a cone, V = \frac{1}{3}\pi r^2 H and C = \pi r \sqrt{r^2+H^2}. The given expression is 3\pi (\frac{1}{3}\pi r^2 H)H^3 + 9(\frac{1}{9}\pi^2 r^4 H^2) = \pi^2 r^2 H^4 + \pi^2 r^4 H^2 = \pi^2 r^2 H^2 (H^2 + r^2). We can check that C^2 H^2 = (\pi r \sqrt{r^2+H^2})^2 H^2 = \pi^2 r^2 (r^2+H^2) H^2. This perfectly matches the evaluated expression.

Related questions on Mensuration

Practice more CDS Elementary Mathematics questions