SOLUTION
Given the question in the question tab, the following are the solution steps to calculate the required measurements.
Step 1: write the given parameters
![\begin{gathered} \text{diameter}=10\operatorname{cm},\text{altitude}=\text{height}=20\operatorname{cm} \\ r=(d)/(2)=(10)/(2)=5\operatorname{cm} \end{gathered}]()
Step 2: Calculate the volume of the right circular cone
![\begin{gathered} V=(\pi r^2h)/(3) \\ V=(\pi*5*5*20)/(3) \\ V=(500\pi)/(3)=523.5987756 \\ V\approx523.5988\operatorname{cm}^3 \end{gathered}]()
Step 3: Calculate the total surface area of the right circular cone
![\begin{gathered} \text{TSA}=\pi r(r+\sqrt[]{h^2+r^2)} \\ \text{TSA}=\pi(5)(5+\sqrt[]{20^2+5^2)} \\ \text{TSA}=5\pi(5+\sqrt[]{400+25)} \\ \text{TSA}=5\pi(5+\sqrt[]{425})=5\pi(5+20.61552813) \\ \text{TSA}=5\pi(25.615528134) \\ \text{TSA}=402.3677749 \\ \text{TSA}\approx402.3678cm^2 \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/2boiam7c4up31hj8rqt1.png)
Hence, the volume and the total surface area of the given right circular cone are approximately 523.5988cm³ and 402.3678cm² respectively