Question

plz give answers ,take your time ,no need to do fast​

Answer 1

1) Let r and h be radius and height of the cyclinder, then C.S.A. = 2πrh

Now, radius is doubled and height is halved.

∴ New radius = 2r and new height = h / 2

New C.S.A. = 2π × 2r × h / 2 = 2pie r h


2) Lateral surface area of a cube =4a^2. , ( where a be the each edge of cube.)

4a^2=100

or a^2=100/4=25

or a=√(25)=5 cms.

Volume of cube= (a)^3= (5 cm)^3=125 cu.cms. Answer.

3) Therefore, in a cylinder, if the radius is halved and the height is doubled, then the volume will be halved.

4) The total surface area of a hollow cylinder is 2π ( r1 + r2 )( r2 - r1 +h), where, r1 is inner radius, r2 is outer radius and h is height.

5) SURFACE AREAS AND VOLUMES (A) Main Concepts and Results
• Cuboid whose length = l, breadth = b and height = h (a) Volumeofcuboid=lbh
(b) Totalsurfaceareaofcuboid=2(lb+bh+hl)
(c) Lateral surface area of cuboid = 2 h (l + b)
(d) Diagonalofcuboid= l2 +b2 +h2
• Cube whose edge = a
(a) Volume of cube = a3
(b) Lateral Surface area = 4a2
(c) Total surface area of cube = 6a2
(d) Diagonal of cube = a 3
• Cylinder whose radius = r, height = h
(a) Volume of cylinder = πr2h
(b) Curved surface area of cylinder = 2πrh
(c) Total surface area of cylinder = 2πr (r + h)
• Cone having height = h, radius = r and slant height = l
(a) Volume of cone = 13πr2h
(b) Curved surface area of cone = πrl
CHAPTER 13
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122
EXEMPLAR PROBLEMS
(c) Total surface area of cone = πr (l + r)
h2 +r2
(a) Volume of sphere = 43 πr3
(b) Surface area of sphere = 4πr2
• Hemisphere whose radius = r (a) Volume of hemisphere = 23 πr3
(b) Curved surface area of hemisphere = 2πr2 (c) Total surface area of hemisphere = 3πr2
(B) Multiple Choice Questions
Write the correct answer
(d) Slantheightofcone(l)= • Sphere whose radius = r
Sample Question 1 : In a cylinder, if radius is halved and height is doubled, the volume will be
(A) same (B) doubled (C) halved Solution: Answer (C)
EXERCISE 13.1
Write the correct answer in each of the following :
1. The radius of a sphere is 2r, then its volume will be
(D) four times
4πr3 3 8πr3 32πr3 (A) 3 (B) 4πr (C) 3 (D) 3
2
2. The total surface area of a cube is 96 cm . The volume of the cube is:
(A) 8 cm3 (B) 512 cm3 (C) 64 cm3 (D) 27 cm3
3. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is :
(A) 4.2 cm (B) 2.1 cm (C) 2.4 cm (D) 1.6 cm 4. In a cylinder, radius is doubled and height is halved, curved surface area will be
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SURFACE AREAS AND VOLUMES 123 (A) halved (B) doubled (C) same (D) fourtimes
r
5. The total surface area of a cone whose radius is 2 and slant height 2l is r
(A) 2πr(l+r) (B) πr(l+ 4) (C) πr(l+r) (D) 2πrl
6. The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of
5:3. The ratio of their volumes is:
(A) 10:17 (B) 20:27 (C) 17:27 (D) 20:37 2
7. The lateral surface area of a cube is 256 m . The volume of the cube is
(A) 512 m3 (B) 64 m3 (C) 216 m3 (D) 256 m3
8. The number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit which is 16 m long, 12m wide and 4 m deep is
(A) 1900 (B) 1920 (C) 1800 (D) 1840
9. The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5m) is
(A) 15m (B) 16m (C) 10m (D) 12m
10. The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is
(A) 1:4 (B) 1:3 (C) 2:3 (D) 2:1
(C)ShortAnswerQuestions withReasoning
Write True or False and justify your answer.
Sample Question 1 : A right circular cylinder just encloses a sphere of radius r as shown in Fig 13.1. The surface area of the sphere is equal to the curved surface area of the cylinder.
Solution : True.
Here, radius of the sphere = radius of the cylinder = r
Diameter of the sphere = height of the cylinder = 2r
Surface area of the sphere = 4πr2
Curved surface area of the cylinder = 2πr (2r) = 4πr2
Sample Question 2 : An edge of a cube measures r cm. If the largest possible right
1 6
circular cone is cut out of this cube, then the volume of the cone (in cm3) is
3 πr .