The figure shown is a rectangular prism. To find the volume, you multiply the height by the area of the base.
The area of the base is calculated as the length times the width. In this case, the length and width are both 20 inches.
Area of the base = 20in x 20in = 400in²
Now, we multiply the area of the base by the height to find the volume:
Volume = 400in² x 10.5in = 4200in³
Therefore, the volume of the figure shown is 4200 cubic inches.
Find the volume of the figure shown.
height is 10.5in
the sides along the base are all 20in
(1 point)
3 answers
ITS A TRIANGULAR PRISM
I apologize for the mistake. For a triangular prism, we need to find the area of the triangular base and then multiply it by the height to find the volume.
The triangular base can be split into two right-angled triangles. Given that the base sides are all 20 inches, this means each leg of the right-angled triangle is 10 inches.
Using the Pythagorean theorem, we can find the height of the right-angled triangle:
h² = 20² - 10²
h² = 400 - 100
h² = 300
h = √300
h = 17.32 inches
The area of each right-angled triangle is ½ x base x height:
Area of each right-angled triangle = 0.5 x 10in x 17.32in = 86.6in²
Since there are two right-angled triangles as the base, the total area of the base is:
Total area of the base = 2 x 86.6in² = 173.2in²
Now, we multiply the area of the base by the height of the prism to find the volume:
Volume = 173.2in² x 10.5in = 1818.6in³
Therefore, the volume of the triangular prism is 1818.6 cubic inches.
The triangular base can be split into two right-angled triangles. Given that the base sides are all 20 inches, this means each leg of the right-angled triangle is 10 inches.
Using the Pythagorean theorem, we can find the height of the right-angled triangle:
h² = 20² - 10²
h² = 400 - 100
h² = 300
h = √300
h = 17.32 inches
The area of each right-angled triangle is ½ x base x height:
Area of each right-angled triangle = 0.5 x 10in x 17.32in = 86.6in²
Since there are two right-angled triangles as the base, the total area of the base is:
Total area of the base = 2 x 86.6in² = 173.2in²
Now, we multiply the area of the base by the height of the prism to find the volume:
Volume = 173.2in² x 10.5in = 1818.6in³
Therefore, the volume of the triangular prism is 1818.6 cubic inches.
1 answer