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

Answer: (C)

26.16 kg

Answer 2

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.