Advertisements
Advertisements
Question
If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is
Options
2 S
4 S
6 S
8 S
Advertisements
Solution
Let,
l →Length of the first cuboid
b → Breadth of the first cuboid
h → Height of the first cuboid
And,
L → Length of the new cuboid
B → Breadth of the new cuboid
H → Height of the new cuboid
We know that,
L = 2l
B = 2b
H=2h
Surface area of the first cuboid,
S = 2(lb + bh +hl )
Surface area of the new cuboid,
S' = 2 (LB + BH + HI .)
=2 [(2l)(2b)+(2b)(2h)+(2h)(2l)]
=2 ( 4lb + 4 bh +4hl)
=4[2(lb+bh+hl)]
= 4S
The surface area of the new cuboid is 4S.
APPEARS IN
RELATED QUESTIONS
A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. What is the area of the glass?
An ice-cream brick measures 20 cm by 10 cm by 7 cm. How many such bricks can be stored in deep fridge whose inner dimensions are 100 cm by 50 cm by 42 cm?
A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that \[\frac{1}{V} = \frac{2}{S}\left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)\]
The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2 = xyz.
The length, breadth, and height of a cuboid are in the ratio 6: 5 : 3. If its total surface area is 504 cm2; find its dimensions. Also, find the volume of the cuboid.
A closed box is cuboid in shape with length = 40 cm, breadth = 30 cm and height = 50 cm. It is made of a thin metal sheet. Find the cost of metal sheet required to make 20 such boxes, if 1 m2 of metal sheet costs Rs. 45.
The ratio between the curved surface area and the total surface area of a cylinder is 1: 2. Find the ratio between the height and the radius of the cylinder.
A room is 22m long, 15m broad and 6m high. Find the area of its four walls and the cost of painting including doors and windows at the rate of Rs.12per m2.
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
