Advertisements
Advertisements
प्रश्न
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is
विकल्प
27 cm2
32 cm2
44 cm2
88 cm2
उत्तर
Length (l), width (b) and height (h) of the rectangular solid are in the ratio 3 : 2 : 1.
So we can take,
(l) = 3x cm
(b) = 2 x cm
(h) = x cm
We need to find the total surface area of the box
Volume of the box,
`V= 48 cm^3`
lbh = 48
(3x)(2x)x = 48
6x3 = 48
x3 = 8
x = 2
Thus,
Surface area of the box,
= 2 (lb+bh+hl)
= 2 [(3x)(2x)+(2x) x +(x)(3x)]
= 2 (11x2)
= 22 x2
= 22 (2)^2
= 88 cm2
Thus total surface area of the box is 88 cm2 .
APPEARS IN
संबंधित प्रश्न
Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.
Hameed has built a cubical water tank with lid for his house, with each other edge 1 .5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of tiles is Rs. 360 per dozen.
A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid?
A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?
A swimming pool is 250 m long and 130 m wide. 3250 cubic metres of water is pumped into it. Find the rise in the level of water.
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 length, breadth, and height of a cuboid (rectangular solid) are 4 : 3: 2.
(i) If its surface area is 2548 cm2, find its volume.
(ii) If its volume is 3000 m3, find its surface area.
A cuboid is 8 m long, 12 m broad and 3.5 high, Find its
(i) total surface area
(ii) lateral surface area
The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15,000, find the height of the hall.
