Calculate the total surface are of a solid cone of slant height 10cm and base diameter 10cm. Use the value
Calculate the total surface are of a solid cone of slant height 10cm and 10cm and base diameter 10cm.use the value 3.14 for^
base area ... π (d/2)^2 ... 3.14 * (10/2)^2
side area ... π (sh)^2 [d / (2 sh)] ... π sh d/2 ... 3.14 * 10 * 10/2
The total surface area of a solid cone can be calculated by adding the lateral surface area and the base area.
1. Calculate the lateral surface area:
The slant height of the cone is 10 cm. The circumference of the base can be calculated using the formula:
circumference = π * diameter
The diameter of the base is 10 cm, so the circumference is:
circumference = π * 10 cm = 10π cm
The formula for the lateral surface area of a cone is:
lateral surface area = π * radius * slant height
The radius of the base can be calculated using the formula:
radius = diameter / 2 = 10 cm / 2 = 5 cm
Using these values, the lateral surface area of the cone is:
lateral surface area = π * 5 cm * 10 cm = 50π cm²
2. Calculate the base area:
The base area of a cone can be calculated using the formula:
base area = π * radius²
Using the radius calculated earlier, the base area is:
base area = π * (5 cm)² = 25π cm²
3. Calculate the total surface area:
The total surface area of the cone is the sum of the lateral surface area and the base area:
total surface area = lateral surface area + base area
total surface area = 50π cm² + 25π cm² = 75π cm²
Therefore, the total surface area of the solid cone is 75π cm² (or approximately 235.62 cm²).
To calculate the total surface area of a solid cone, we need to find the sum of the lateral surface area and the base area.
Lateral Surface Area:
The lateral surface area of a cone can be calculated using the formula:
Lateral Surface Area = π * radius * slant height
Given that the base diameter is 10cm, the radius can be calculated as half of the diameter:
radius = 10cm / 2 = 5cm
The slant height is given as 10cm.
Substituting these values into the formula, we get:
Lateral Surface Area = π * 5cm * 10cm
Base Area:
The base area of a cone is given by the formula:
Base Area = π * radius^2
Substituting the radius value we calculated earlier, we get:
Base Area = π * (5cm)^2
Calculating the values:
Lateral Surface Area = 3.14 * 5cm * 10cm
Base Area = 3.14 * (5cm)^2
Now, we can calculate the total surface area by adding the lateral surface area and the base area:
Total Surface Area = Lateral Surface Area + Base Area
Substituting the calculated values into the equation, we get:
Total Surface Area = (3.14 * 5cm * 10cm) + (3.14 * (5cm)^2)
Calculating the total surface area will give you the final answer.