NCERT Maths Question with Solutions for class 9

 NCERT Maths Question with Solutions for class 9

Q The base of a right triangle is 8 cm and hypotenuse is 10 cm, find its area

 

 

 

Q. Find the area of an equilateral triangle with side 2√3 cm.

= 3√3

Consider √3 = 1.732

= 3 × 1.732    = 5.196 cm²       Therefore, the area of an equilateral triangle is 5.196 cm²   (if answer is required in points or else 3√3 cm²  answer is enough)

Q. What is the lateral surface area of cuboid dimensions l x b x h

 

Q. Slant height of a cone is 34 cm and base diameter is 32 cm. find the height of the cone.

 

Q5. In a triangle ABC, D, E and F are the midpoints of AB, BC and AC respectively and the length of AB, BC and AC respectively 5 cm, 4 cm and 11 cm, find the perimeter of the triangle DEF

 

Q6. Two sides of a triangle are 13 cm and 14 cm and its perimeter is 36 cm. Find the area of this triangle.

 

Let the length of the third side be x cm.

Length of other two sides is 13 cm and 14 cm.

Now, Perimeter of triangle = Sum of all sides = 36 cm.

⇒13+14+x=36    ⇒27+x=36      ⇒x=36−27    ⇒x=9cm  

Thus, the length of third side is 9 cm.

The sides of triangle are

a=13, b=14, c= 9

Semi-perimeter s=1/2(a+b+c)=1/2(13+14+9)=18

Area, A = √s(s−a)(s−b)(s−c)

A=√18(18−13)(18−14)(18−9)     =√18(5)(4)(9)   = = 2 x 3 x √90   

The area of this triangle is 6√90cm²

 

Q.7 Find the radius of a sphere whose surface area is 154cm²

Q.8 If V and S be the surface area and volume respectively of a cuboid of dimension L x B x H, then show that S/2V = 1/L + 1/B + 1/H

 

Q9. ABCD is a parallelogram in which AB is produced to E, so that BE = AB. Prove that ED bisects BC.

 

Q.10 In a parallelogram show that the angle bisectors of two adjacent angles intersect Perpendicularly. (Note In Mathematics, a perpendicular is defined as a straight line that makes the right angle (90 degrees) with the other line. In other words, if two lines intersect each other at the right angle, then the lines are perpendicular to each other)

Note: A property of that parallelogram says that if a parallelogram has all sides equal, then their diagonal bisector intersects perpendicularly. An angle bisector is a ray that splits an angle into two consecutive congruent, smaller angles.

 

Q. The angle of a quadrilateral are respectively 100^o,30^o,92^o,X⁰. Find the value of X

Then, by angle sum property of quadrilateral,

100^o+30^o+92^o+x^o=360^o

X⁰ = 360⁰  - 222⁰ = 138⁰

 

Q.11 Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.

 

Q.12 The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold?

                          (Note The volume of a cylinder of base radius, r and height, h = πr²h)

= 34650/1000 (Since 1000 cm³ = 1 L)

= 34.65 L

 

Q13 In a parallelogram ABCD, E and F are the mid-point of the sides AB and CD respectively. AF and CE meet the diagonal BD of length 12 cm at P and Q respectively.  Find the length of PQ.

 

Q.14 ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that quadrilateral PQRS is a rhombus.

Q.15. A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. find its total surface area.

 

Q. 15 The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases