Advertisements
Advertisements
प्रश्न
The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is `5sqrt(5)` cm. Its surface area is
पर्याय
361 cm2
125 cm2
236 cm2
486 cm2
उत्तर
236 cm2
Let l, b and h be the length, breadth and height of the cuboid.
Then,
l + b + h = 19
⇒ ( l + b + h )2 + 2 (lb + bh + lh) = 36
`⇒ (5sqrt(5) + 2("lb" + "bh" + "lh") = 361`
⇒ 2 (lb + bh + lh) = (361 - 125)
`⇒ 2("lb" + "bh" +"lh") = 236 "cm"^2`
Hence, the surface area of the cuboid is 236 cm2
APPEARS IN
संबंधित प्रश्न
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is `14/3` m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.
Find the ratio of the volumes of a cylinder and a cone having equal radius and equal height.
(A)1 : 2 (B) 2 : 1 (C) 1 : 3 (D) 3 : 1
Water flows at the rate of 10 m / minute through a cylindrical pipe 5 mm in diameter . How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm.
The radius of the base of a right circular cone of semi-vertical angle α is r. Show that its volume is \[\frac{1}{3} \pi r^3\] cot α and curved surface area is πr2 cosec α.
A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.
A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.
The slant height of a bucket is 45 cm and the radii of its top and bottom are 28 cm and 7 cm, respectively. The curved surface area of the bucket is
The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is
A rectangular examination hall having seats for 500 candidates has to be built so as to allow 4 cubic metres of air and 0.5 square metres of floor area per candidate. If the length of hall be 25 m, find the height and breadth of the hall.
The radius of a metal sphere is 3 cm. The sphere is melted and made into a long wire of uniform circular cross-section, whose length is 36 cm. To calculate the radius of wire, complete the following activity.
Radius of the sphere = `square`
Length of the wire = `square`
Let the radius of the wire by r cm.
Now, Volume of the wire = Volume of the `square`
`square` = `square`
r2 × `square` = `square` × `square`
r2 × `square` = `square`
r = `square`
Hence, the radius of the wire is `square` cm.
