Question

The weight of a solid cone having diameter 14 cm and vertical height 51 cm is _______ if the material of solid cone weighs 10 grams per cubic cm.

• A. 16.18 kg
• B. 17.25 kg
• C. 26.16 kg
• D. 71.40kg

Answer 1

The Correct Option is C

The correct option is (C): 26.16 kg
To find the weight of the solid cone, we can use the formula for the volume of a cone and then multiply it by the density of the material.

Steps to Solve:

1. **Formula for the Volume of a Cone**:
\[V = \frac{1}{3} \pi r^2 h \]
  Where:
  \( r \) = radius of the cone
   \( h \) = height of the cone

2. Given Values:
  - Diameter = 14 cm, so the radius \( r = \frac{14}{2} = 7 \) cm
  - Height \( h = 51 \) cm
  - Density of the material = 10 grams/cm³

3. Calculating the Volume:
  \[V = \frac{1}{3} \pi (7^2)(51)\]
  \[V = \frac{1}{3} \pi (49)(51)\]
  \[V = \frac{1}{3} \pi (2499)\]
  \[V \approx \frac{1}{3} \times 3.14 \times 2499\]
  \[V \approx \frac{1}{3} \times 7847.86 \approx 2615.95 \, \text{cm}^3\]

4. Calculating the Weight:
  \[\text{Weight} = \text{Volume} \times \text{Density}\]
  \[\text{Weight} = 2615.95 \, \text{cm}^3 \times 10 \, \text{grams/cm}^3\]
  \[\text{Weight} \approx 26159.5 \, \text{grams}\]

5. Converting grams to kilograms:
  \[\text{Weight} \approx \frac{26159.5}{1000} \approx 26.16 \, \text{kg}\]

Conclusion:
The weight of the solid cone is approximately 26.16 kg.