Cuboidal metal block length 38 CM and breadth 25 cm has total surface area 3790 CM sq unit find it's volume
Answers
Given data : Cuboidal metal block length 38 cm breadth 25 cm has total surface area 3790 cm².
To find : Find volume of the cuboidal metal block ?
Solution : Here, a/c to given data;
- Length of the block = 38 cm
- Breadth of the block = 25 cm
- total surface area of the block = 3790 cm²
Firstly, we have to find out height of the block.
By, formula total surface of the cuboid;
➜ surface area = 2LB + 2LH + 2HB
{where,
- L is length
- B is breadth
- H is height }
➜ surface area of the block = 2LB + 2LH + 2HB
➜ 3790 = 2 * 38 * 25 + 2 * 38 * H + 2 * H * 25
➜ 3790 = 2 * 950 + 76 * H + 50 * H
➜ 3790 = 1900 + 126 * H
➜ 126 * H = 3790 - 1900
➜ 126 * H = 1890
➜ H = 1890/126
➜ H = 15 cm
Now, by formula of volume of cuboid;
➜ volume of the block = length * breadth * height
➜ volume of the block = 38 * 25 * 15
➜ volume of the block = 950 * 15
➜ volume of the block = 14250 cm³
Answer : Hence, the volume of the cuboidal metal block is 14250 cm³.
{Verification : surface area of the block = 3790 cm²
➜ surface area of the block = 2LB + 2LH + 2HB
➜ surface area of the block = 2 * 38 * 25 + 2 * 38 * 15 + 2 * 15 * 25
➜ surface area of the block = 2 * 950 + 2 * 570 + 2 * 375
➜ surface area of the block = 1900 + 1140 + 750
➜ surface area of the block = 3040 + 750
➜ surface area of the block = 3790 cm²
Hence it's verified. }
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