Calculation of the Volume of a Toy in the Form of a Cone Mounted on a Hemisphere
In this article, we will delve into the details of calculating the volume of a toy that is designed in the form of a cone mounted on a hemisphere. The toy's specifications are as follows: the diameter of the base of the cone is 7 cm, and its height is 15.5 cm. The diameter of the hemisphere is also 7 cm. We will use the value of pi as 3.14 to perform our calculations.
Dimensions and Formulas
The toy's dimensions are as follows:
Radius of the cone: 3.5 cm (since the diameter is 7 cm) Height of the cone: 15.5 cm Radius of the hemisphere: 3.5 cm (since the diameter is 7 cm)The volume of a cone is given by the formula: ( V_{cone} frac{1}{3} pi r^2 h ), where ( r ) is the radius of the base, and ( h ) is the height.
The volume of a hemisphere is given by the formula: ( V_{hemisphere} frac{2}{3} pi r^3 ).
Calculating the Volume
To find the total volume of the toy, we need to add the volume of the cone and the volume of the hemisphere.
Step 1: Calculate the Volume of the Cone
Step 2: Calculate the Volume of the Hemisphere
Step 3: Add the Volumes Together
The calculations can be summarized as follows:
Volume of the Cone
Using the formula for the volume of a cone:
[begin{align*} V_{cone} frac{1}{3} pi r^2 h frac{1}{3} times 3.14 times (3.5)^2 times 15.5 3.14 times frac{1}{3} times 12.25 times 15.5 3.14 times 61.925 194.5595 , text{cm}^3 end{align*}]Volume of the Hemisphere
Using the formula for the volume of a hemisphere:
[begin{align*} V_{hemisphere} frac{2}{3} pi r^3 frac{2}{3} times 3.14 times (3.5)^3 3.14 times frac{2}{3} times 42.875 3.14 times 28.5833 89.1179 , text{cm}^3 end{align*}]Total Volume of the Toy
[begin{align*} V_{total} V_{cone} V_{hemisphere} 194.5595 89.1179 283.6774 , text{cm}^3 end{align*}]Conclusion
The total volume of the toy is approximately 283.6774 cm3. This calculation is based on the dimensions provided and the formulas for the volumes of a cone and a hemisphere.
Related Questions
If you have any other questions or need further assistance with geometric calculations, feel free to ask. We can explore more formulas and examples to deepen your understanding.