If the dimension of a right rectangular prism are 7cm,9cm and 3cm,then find
(A) Its total surface area
(B) Its volume
(C) the length of its diagonal
a = 2(7*9+7*3+9*3) = 222
v = 7*9*3 = 189
d = √(7^2+9^2+3^2) = √139
I don't understand the diagonal how to find it
Maths is hard😫
To find the total surface area of a right rectangular prism, we need to determine the areas of all its faces and then add them together.
The total surface area (TSA) can be calculated using the formula:
TSA = 2lw + 2lh + 2wh
Given the dimensions of the right rectangular prism:
Length (l) = 7 cm
Width (w) = 9 cm
Height (h) = 3 cm
(A) Total Surface Area:
TSA = 2lw + 2lh + 2wh
Substituting the values into the formula, we have:
TSA = 2(7)(9) + 2(7)(3) + 2(9)(3)
TSA = 126 + 42 + 54
TSA = 222 cm²
Therefore, the total surface area of the right rectangular prism is 222 square centimeters.
To find the volume of a right rectangular prism, we need to multiply the length, width, and height together.
(B) Volume:
Volume = lwh
Substituting the given values, we have:
Volume = 7(9)(3)
Volume = 189 cm³
Therefore, the volume of the right rectangular prism is 189 cubic centimeters.
To find the length of the diagonal of the right rectangular prism, we can use the Pythagorean theorem since the length, width, and height form a right-angled triangle.
(C) Length of Diagonal:
Using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides, we have:
Diagonal² = Length² + Width² + Height²
Diagonal² = 7² + 9² + 3²
Diagonal² = 49 + 81 + 9
Diagonal² = 139
Taking the square root of both sides to solve for the diagonal, we have:
Diagonal = √139
Therefore, the length of the diagonal of the right rectangular prism is approximately √139 cm.
Don't worry, I can explain it to you. The diagonal of a rectangular prism is the line that goes from one corner of the prism to the opposite corner, through the center of the prism.
To find the length of the diagonal in this case, we can use the Pythagorean theorem, which says that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
So, for this rectangular prism, we can consider the three dimensions to be the three sides of a right triangle. Let's call the length of the diagonal "d", and the three sides of the prism "a", "b", and "c". Then, using the Pythagorean theorem, we have:
d^2 = a^2 + b^2 + c^2
Substituting the values we know:
d^2 = 7^2 + 9^2 + 3^2
d^2 = 49 + 81 + 9
d^2 = 139
Now we just need to take the square root of both sides to find "d":
d = sqrt(139) ≈ 11.79
So, the length of the diagonal of the right rectangular prism is approximately 11.79 cm.
(A) Its total surface area
Well, if we have a right rectangular prism with dimensions 7 cm, 9 cm, and 3 cm, we can calculate the total surface area by adding up the areas of all six faces. So, let's get to the math circus!
First, let's calculate the area of the top and bottom faces. The length and width are given as 7 cm and 9 cm, respectively, so the area is 7 cm * 9 cm = 63 cm². Since there are two faces, we multiply this by 2 to get 126 cm².
Next, let's calculate the area of the front and back faces. The length and height are 7 cm and 3 cm, respectively, so the area is 7 cm * 3 cm = 21 cm². Again, since there are two faces, we multiply this by 2 to get 42 cm².
Finally, let's calculate the area of the two side faces. The width and height are 9 cm and 3 cm, so the area is 9 cm * 3 cm = 27 cm². And just like before, since there are two faces, we multiply this by 2 to get 54 cm².
To find the total surface area, we add up the areas of all six faces: 126 cm² + 42 cm² + 54 cm² = 222 cm².
So, the total surface area of the right rectangular prism is 222 cm².
(B) Its volume
To calculate the volume of a right rectangular prism, we need to multiply its length, width, and height. In this case, the dimensions are given as 7 cm, 9 cm, and 3 cm, so the volume is 7 cm * 9 cm * 3 cm = 189 cm³.
So, the volume of the right rectangular prism is 189 cm³. It seems like we have a pretty boxy performer here!
(C) The length of its diagonal
Finding the length of the diagonal is quite a fantastic trick! Let's use the Pythagorean theorem to solve this, shall we?
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In our case, we can imagine the length, width, and height of the prism as the three sides of a right-angled triangle, with the diagonal being the hypotenuse.
Using the formula, we can find the length of the diagonal:
Diagonal² = Length² + Width² + Height²
Diagonal² = 7 cm² + 9 cm² + 3 cm²
Diagonal² = 49 cm² + 81 cm² + 9 cm²
Diagonal² = 139 cm²
To find the length of the diagonal, we need to take the square root of both sides:
Diagonal = √(139 cm²)
Using a bit of calculator magic, we find that the length of the diagonal is approximately 11.80 cm. Voilà!
So, the length of the diagonal of the right rectangular prism is approximately 11.80 cm. That's one diagonal that likes to stretch!