Find the lateral area and surface area of each solid to the nearest square unit.
Four exercises have various figures. Exercise 15 is a rectangular prism with length of 10 yards, width of 7.5 yards and height of 5 yards.
Exercise 16 is a square pyramid with a base edge of 9 meters, height of 13.5 meters and slant height of 13.8 meters.
Exercise 17 is a cone with a radius of 7 centimeters, height of 14 centimeters and slant height of 15.7 centimeters.
Exercise 18 is a cylinder with a length of 22 inches and a diameter of 22 inches.
Find the volume of each solid. When using π round to the nearest cubic unit.
Four exercises have various figures. Exercise 19 is a square pyramid with a base edge of 1 foot, height of 0.75 feet and slant height of 0.9 feet.
Just use your formulas
cone: A = πr(r+s)
pyramid: A = b^2 + 4*(bs/2)
cylinder: A = 2πr(r+h)
prism: A = 2(xy+xz+yz)
To find the lateral area and surface area of each solid, we need to know the formulas for each shape.
1. Rectangular Prism:
- Lateral Area: The lateral area of a rectangular prism is given by the formula:
Lateral Area = 2 * (length * height + width * height)
Plugging in the values: Lateral Area = 2 * (10 * 5 + 7.5 * 5)
- Surface Area: The surface area of a rectangular prism is given by the formula:
Surface Area = 2 * (length * width + length * height + width * height)
Plugging in the values: Surface Area = 2 * (10 * 7.5 + 10 * 5 + 7.5 * 5)
2. Square Pyramid:
- Lateral Area: The lateral area of a square pyramid is given by the formula:
Lateral Area = base edge * slant height / 2
Plugging in the values: Lateral Area = 9 * 13.8 / 2
- Surface Area: The surface area of a square pyramid is given by the formula:
Surface Area = base edge * (base edge + sqrt(base edge^2 + 4 * height^2))
Plugging in the values: Surface Area = 9 * (9 + sqrt(9^2 + 4 * 13.5^2))
3. Cone:
- Lateral Area: The lateral area of a cone is given by the formula:
Lateral Area = π * radius * slant height
Plugging in the values: Lateral Area = π * 7 * 15.7
- Surface Area: The surface area of a cone is given by the formula:
Surface Area = π * radius * (radius + slant height)
Plugging in the values: Surface Area = π * 7 * (7 + 15.7)
4. Cylinder:
- Lateral Area: The lateral area of a cylinder is given by the formula:
Lateral Area = 2 * π * radius * height
Plugging in the values: Lateral Area = 2 * π * 11 * 22
- Surface Area: The surface area of a cylinder is given by the formula:
Surface Area = 2 * π * radius * (radius + height)
Plugging in the values: Surface Area = π * 11 * (11 + 22)
Now, we can calculate the lateral areas and surface areas using the above formulas.
For Exercise 15 (Rectangular Prism):
Lateral Area = 2 * (10 * 5 + 7.5 * 5)
Surface Area = 2 * (10 * 7.5 + 10 * 5 + 7.5 * 5)
For Exercise 16 (Square Pyramid):
Lateral Area = 9 * 13.8 / 2
Surface Area = 9 * (9 + sqrt(9^2 + 4 * 13.5^2))
For Exercise 17 (Cone):
Lateral Area = π * 7 * 15.7
Surface Area = π * 7 * (7 + 15.7)
For Exercise 18 (Cylinder):
Lateral Area = 2 * π * 11 * 22
Surface Area = π * 11 * (11 + 22)
For Exercise 19 (Square Pyramid):
Lateral Area = 1 * 0.9 / 2
Surface Area = 1 * (1 + sqrt(1^2 + 4 * 0.75^2))
Please note that in the case of calculating surface area, you can round the values to the nearest square unit. Also, in the case of using π, round the volume to the nearest cubic unit.