surface area and volumes
DESCRIPTION
Surface Area And VolumesTRANSCRIPT
Made By: Saurav Kumar Singh Class: IX – F
SURFACE AREA AND
VOLUMES
1) A cylindrical glass can contain 108π cm3 of water. The base of the glass has a radius of 3 cm. What is the height
of the glass?
(a)12 cm (b) 6 cm(c) 9cm (d) 3 cm
The correct answer is 12 cm.Solution:
The base of the cylindrical glass has a radius = 3 cm
Area of the base will be πr²= 9π cm²
Volume of the cylindrical glass = πr²h
The height of the cylindrical glass = v/πr² = 108π/9π = 12 cm.
The correct option is (A).
2) A silver gift box is cuboidal in shape. The dimensions of the box are 6 cm,
4 cm and 5 cm. What will be the volume of the gift box?
(a) 24 cm² (b) 24cm³
(c) 120 cm² (d) 120cm³
The correct answer is 120cm³
Solution:
Length of the cuboidal gift box = 6cm
Width of the cuboidal gift box = 4cm
Height of the cuboidal gift box = 5cm
The volume of the gift box = length × width × height
= 6cm*4cm*5cm = 120cm³.
The correct option is (d).
3) The volume of a rectangular prism 10 dm × 4 dm × 2 m is
(a) 800dm (b) 800dm²
(c) 800dm³ (d) 800m
The correct answer is 800dm³
Solution:
Length (l) of the rectangular prism = 10 dm
Width (w) of the rectangular prism = 4 dmHeight (h) of the rectangular prism = 2 m= 2 × 10 dm [10 dm = 1 m] =20dmVolume of the prism = l × w × h10dm*4dm*20dm= 800dm³.The correct option is (c).
4) The cone and a cylinder have a same base area and the same volume, then what is the ratio of their respective
height?
(a) 1:1 (b) 3:1
(c) 4:9 (d) 9:1
The correct answer is 3:1
Solution:
Since the cone and the cylinder have the same base area, their radii are the same.
Therefore, let radius of cone = radius of cylinder= r
Let h1 and h2 be the height of the cone and the cylinder respectively.
Therefore, volume of the cone= 1/3πr²h1
Volume of the cylinder = πr²h2
It is given that the volumes of the cone and the cylinder are equal
Therefore, 1/3πr²h1= πr²h2Þ h1= 3h2 => h1/h2 = 3/1Þ Thus, the ratio of the heights of the cone and the cylinder is 3:1.Þ The correct option is (b).
5) A rectangular box is 16cm high, 10cm long and 5cm broad is to be painted with enamel, What is the total area to be
painted ?
(a) 150cm² (b) 290cm²
(c) 300cm² (d) 580cm²
The correct answer is 580cm²
Solution:
The total area to be painted=the surface area of the rectangular box
= 2(lb + bh + lh).
= 2(10×5 + 5×16 + 10×16).
= 2( 50+ 80+160) = 580cm².
The correct option is (d).
7) A rectangular prism is made by joining some cubes as shown in the figure, the volume of each small cube 1cm³.
(a) 32cm³ (b) 36cm³
(c) 42cm³ (d) 46cm³
The correct answer is 36cm³
Solution:
Length of each side of small cube = 1 cm
Volume of each cube = 1 cm3
The given rectangular prism is made up of 36 small equal sized cubes.
Volume of 36 cubes = 36 × 1 = 36 cm3
Volume of the rectangular prism = volume of 36 cubes = 36 cm3.
The correct option is (b).
8) What is the length of the edge of the cube whose volume is 2744 cm3?
(a) 14cm (b) 12cm
(c) 7cm (d) 6cm
The correct answer is 14cm.
Solution:
Let the length of the edge of the cube be ‘a’.
It is known that volume of cube = (edge)³
Therefore, (a)³ = 2744cm³Þ a = ³√2744cmÞ a = ³√2×2×2×7×7×7cmÞ a = 2×7cm = 14cm.
The correct option is (a).
9) Which of the container has the same volume as the given container ?
The correct answer is figure 2.
This is a simple question so students should try it
self.
10) A box of the shape of a rectangular prism is formed by fitting together 10 cubes. The volume of each cube is 8 cm3.
The volume of the box, so formed is
(a) 50cm³ (b) 60cm³
(c) 70cm³ (d) 80cm³
The correct answer is 80³.
Solution:
Volume of 1 cube = 8 cm3
Number of cubes joined together to form the box = 10
Thus, volume of 10 cubes = 10 × 8 cm3 = 80 cm3
Thus, volume of the box = volume of 10 cubes = 80 cm3
The correct answer is (d).
THE END.