A pentagon may be formed by joining 5 points lying on a plane. However, if we choose 3 or more points which are collinear, then the pentagon will not be formed.

Therefore, here we have 13 non-collinear points and 7 collinear points.

Number of pentagons that can be drawn= ^{13}C_{5}+ ^{13}C_{4}^{7}C_{1}+ ^{13}C_{3}^{7}C_{2}

SURFACE AREA AND VOLUME- CLASS 9

Basic level

1. A cuboidal water tank is 6m long, 5 m wide and 4.5 m deep. How many litres of water can it be hold? (1 m3 = 1000 litres).

(Ans. 135000 litres)

2. Find the radius and volume of a sphere whose surface area is 154 cm2.

(Ans. radius = 3.5 cm and volume = 179𝟐𝟑 𝒄𝒎𝟑)

3. Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

(Ans. 165 cm2).

4. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of sheet is required for the same? (Ans. 7.48 m2)

5. How many planks each of which is 2 m long, 3 cm broad and 4 cm thick can be cut-off from a wooden block 6 m long, 18 cm broad and 44 cm thick?

(Ans. 198).

6. Curved surface area of a cone is 306 cm2 and its slant height is 14 cm. Find (i) radius of the base (ii) total surface area of the cone

(Ans. r = 7cm and TSA = 462 cm2)

7. The radius and slant height of a cone are in the ratio 4:7. If its curved surface area is 792 cm2, find its radius. (Ans. r = 12 cm)

8. The lateral surface area of a cube is 576 cm2. Find its volume and total surface area.

(Ans. Volume = 1728 cm3 and TSA = 864 cm2)

Intermediate level

9. A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface area of the solid so formed.

10. The resident of society decided to paint the hall of cancer detective center in their premises. If the floor of the cuboidal hall has a perimeter equal to 260 m and height 6 m then

a. Find the cost of painting of its four walls at the rate of Rs. 9 per m2.

b. What is the amount contributed by 50 people?

c. Which value is depicted by the residents?

11. A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 am and 6 cm respectively. Find the volume of the copper used in making the pipe.

(Ans. V= 10560 cm3)

12. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.

(Ans. 20:27, 10:9)

13. The radius and the height of a right circular cone are in the ratio 5:12. If its volume is 314

cm3, find the slant height and the radius.(Use 𝜋 = 3.14)

(Ans. = 13m, 5m)

14. How many spherical bullets can be made out of a solid cube of lead whose edge measures

44 cm, each bullet being 4 cm in diameter?

(Ans. 2541)

15. Find the volume of the largest right circular cone that can be cut out of a cube whose

edge is 9 cm.

(Ans. 190.93 cm3)

16. A solid cylinder has a total surface area 462 cm2. Its curved surface area is one-third of

the total surface area. Find the volume of the cylinder.

(Ans. 539 cm3)

17. A rectangular sheet of paper 30 cm x 18 cm can be transformed into the curved surface

area of a right circular cylinder into two ways either by rolling the paper along its length

or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus

formed.

(Ans. 5:3)

18. The volume of metallic cylinder pipe is 748 cm3. Its length is 14 cm and its external

radius is 9 cm. Find its thickness. (Ans. thickness of the pipe = 1 cm)

Advanced level

19. The diameter of a sphere is decreased by 25%. By what percent its surface area

decreased? (Ans. 43.75%)

20. If V is the volume of a cuboid of dimensions l, b, h and S is its surface area, then prove

that

V

1

=

S

2

l b h

1 1 1

.

21. A cone of height 24 cm has a curved surface area 550 cm2. Find its volume.

(Ans. volume = 1232 cm3)

22. The surface area of a sphere of radius 5 cm is five times the curved surface area of a cone

of radius 4 cm. Find the height and volume of the cone.

(Ans. height = 3 cm and volume = 50.29 cm2)

23. A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all

around to a width of 5 m to form an embankment. Find the height of embankment.

(Ans. 4.66 m)

24. The volume of the two spheres are in the ratio 64:27. Find the difference of their surface

areas, if the sum of their radii is 7cm.

(Ans. 88 cm2)

25. A semi-circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find

the depth and capacity of cup.

(Ans. Depth = 12.12 cm, Capacity = 622.26 cm3)

4.during maths lab activity each student was given four broom sticks of lenths 8 cm , 8cm, 5cm ,5cm to make different types of quadrilaterals .

a. how many quadrilaterals can be formed using these sticks

b. name the types of quadrilaterals formed

c. while doing this activity which value is depicted

one of the factors of (1-3y)

^{2}+(9y^{2}-1) is:(A) (1-3y) ; (B) (3-y) ; (C) (3y+1) ;(D)( y-3)

^{3}-6x^{2}-11x+4.Also find third zero of polynomial>Q) In a flood hitted area, the volunteers of NSS erected a conical tent made of tarpaulin. The vertical height of the conical tent is 4 m and the base diameter is 6 m. If the width of tarpaulin is 1.5 m then

a) Find the length of the tarpaulin used, assuming that 10% extra material is required for stiching margins and wastage in cutting. ( Take pi = 3.14 )

b) Which value is depicted by the volunteers ?

AB is a chord of a circle with radius ‘r’. If P is any point on the circle such that ∠APB is a right angle , then AB is equal to ??

how to solve this question & plz tell the method for solving

what is the formula of (a+b+c) whole cube

the dimensions of acuboid are in the ratio 3:2:2 and the lateral surface area of the cuboid is 200m

^{2}. the outer surface of cuboid is painted with enamel at the rate of @ 10 per m^{2}. find the total coast of painting the outer surface of cuboid .Integral zeroes of the polynomial (x+3)(x-7) are

a) -3 , -7 b) 3,7 c) -3,7 d) 3,-7

20 points lie on a plane, out of which 7 points are collinear. Find the number of pentagons that can be drawn?

15373

15474

15383

12298

Time Spent: 1040 seconds

Hide Solution

A pentagon may be formed by joining 5 points lying on a plane. However, if we choose 3 or more points which are collinear, then the pentagon will not be formed.

Therefore, here we have 13 non-collinear points and 7 collinear points.

Number of pentagons that can be drawn

=^{13}C_{5}+^{13}C_{4}^{7}C_{1}+^{13}C_{3}^{7}C_{2}= 1287 + 715 × 7 + 286 × 21 = 1287 + 5005 + 6006 = 12298

The correct answer is D.

how is it

^{13}C_{4}^{7}C_{1}+^{13}C_{3}^{7}C_{2}_{pls can u explain why isit so?}_{}