a rectangular block has a square base of area 49cm square its height is 10 cm find its total surface area
If the base is a square of area 49, then each side is 7 cm
so look at the block, you have 2 squares + 4 equal surfaces on the sides
Surface area = 2(49) + 4(7)(10)
= 378 cm^2
btw, I don't understand your previous post, it looks incomplete
Well, isn't that a block-tacular question! Let's break it down, shall we?
First things first, we need to find the dimensions of the square base. Since the area of the base is 49 cm² and a square has equal sides, we can take the square root of 49 to find the length of each side. So, the length of each side of the square base is 7 cm.
Now, let's move on to the total surface area. A rectangular block has six faces, and each face contributes to the total surface area. The four faces that make up the sides of the block are all the same size, so we can easily calculate their area.
Since the length of the base is 7 cm and the height is 10 cm, the area of each side face is 7 cm multiplied by 10 cm, which gives us 70 cm² per face. Simple math, right?
Moving on to the top and bottom faces, we have two identical square faces. The area of each square face is simply the length of a side squared. In this case, it's 7 cm times 7 cm, which equals 49 cm² per face.
Now, adding up all the areas, we have four side faces with a total combined area of 280 cm², plus two top and bottom faces with a total combined area of 98 cm².
To find the total surface area, we simply add up these areas. So, the surface area of the rectangular block is 280 cm² + 98 cm², which gives us a grand total of 378 cm².
Voila! There you have it, the total surface area of the rectangular block is 378 cm².
To find the total surface area of the rectangular block, we need to consider all six faces: the two bases and the four lateral faces.
1. Find the side length of the square base:
Since the base is square and its area is 49 cm², we can find the side length by taking the square root of the area:
side length = √(area of square base) = √49 cm² = 7 cm
2. Calculate the area of the base:
The base is a square, so its area is given by:
area of base = side length * side length = 7 cm * 7 cm = 49 cm²
3. Calculate the area of the four lateral faces:
The lateral faces of the block are all rectangles with the same dimensions, so we can calculate the area of one of them and then multiply by 4 to get the total area.
The dimensions of the lateral faces are the height of the block and the side length of the square base:
area of one lateral face = height * side length = 10 cm * 7 cm = 70 cm²
total area of the four lateral faces = 4 * area of one lateral face = 4 * 70 cm² = 280 cm²
4. Calculate the total surface area:
The total surface area of the rectangular block is the sum of the areas of the two bases and the four lateral faces:
total surface area = 2 * area of base + total area of the four lateral faces
total surface area = 2 * 49 cm² + 280 cm² = 98 cm² + 280 cm² = 378 cm²
Therefore, the total surface area of the rectangular block is 378 cm².
To find the total surface area of a rectangular block, you need to consider the area of all its faces.
In this case, the rectangular block has a square base with an area of 49 cm². Since the base is square, each side of the square has the same length.
Now, let's find the length of each side of the base:
Area of a square = side × side
49 cm² = side × side
To find the length of the sides, we can take the square root of both sides:
√(49 cm²) = √(side × side)
7 cm = side
So, each side of the square base is 7 cm.
Now, let's calculate the total surface area of the rectangular block.
1. Surface area of the base:
Since the base is a square, the surface area of the base is equal to the area of the square, which is 49 cm².
2. Surface area of the four lateral faces:
There are four lateral faces of the rectangular block. Each lateral face is in the shape of a rectangle and has a length equal to the length of the side of the square base (which is 7 cm) and a height equal to the height of the block (which is 10 cm).
So, the surface area of each lateral face is length × height = 7 cm × 10 cm = 70 cm².
Since there are four lateral faces, the total surface area of the four lateral faces is 4 × 70 cm² = 280 cm².
3. Surface area of the top face and bottom face:
The top and bottom faces are also in the shape of a square, each with an area of 49 cm².
To find the total surface area, add up the surface area of all the faces:
Total surface area = surface area of the base + surface area of the four lateral faces + surface area of the top face + surface area of the bottom face
Total surface area = 49 cm² + 280 cm² + 49 cm² + 49 cm²
Total surface area = 427 cm²
Therefore, the total surface area of the rectangular block is 427 cm².