Advertisements
Advertisements
Question
The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is ` 5 sqrt(5)` cm. Its surface area is
Options
361 cm2
125 cm2
236 cm2
486 cm2
Advertisements
Solution
Let,
l → Length of the cuboid
b → Breadth of the cuboid
h → Height of the cuboid
We have,
l + b + h = 19 cm , diagonal of the cuboid
`( sqrt(l^2 + b^2 +h^2)) = 5 sqrt(5) cm `
We are asked to find the surface area
So, the surface area,
= 2 (lb + bh + hl )
= (l + b +h )2 - ( l2 + b2 + h2 )
`=(l + b+ h) - ( sqrt (l^2 + b^2 + h^2 ))^2`
`=19^2 - (5sqrt(5))^2`
=361-125
=236 cm2
Thus, the surface area is 236 cm2
APPEARS IN
RELATED QUESTIONS
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm in following figure. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2. Find the total expenses required for polishing and painting the surface of the bookshelf.
A cuboidal wooden block contains 36 cm3 wood. If it be 4 cm long and 3 cm wide, find its height.
Find the weight of solid rectangular iron piece of size 50 cm × 40 cm × 10cm, if 1 cm3 of iron weighs 8 gm.
The volume of a cuboidal box is 48 cm3. If its height and length are 3 cm and 4 cm respectively, find its breadth.
If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is
The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm2, find the length, the breadth and the height of the solid.
A solid cuboid of metal has dimensions 24 cm, 18 cm, and 4 cm. Find its volume.
The height of a rectangular solid is 5 times its width and its length is 8 times its height. If the volume of the wall is 102.4 cm3, find its length.
How much sheet metal is required to make a closed rectangular box of length 1.5 m, breadth 1.2 m, and height 1.3 m?
The dimensions of a hall is 10 m × 9 m × 8 m. Find the cost of white washing the walls and ceiling at the rate of ₹ 8.50 per m2
