Geometry
- Learn Trigonometry in easy way Watch this video std 10th
- In the adjoining figure, seg QR is a chord of the circle with centre O. P is the midpoint of the chord QR. Theorems which are useful to find solution: i. The segment joining the centre of a circle and the midpoint of a chord is perpendicular to th... 1
- What is the distance between two parallel tangents of a circle having radius 4.5 cm? Justify your answer. Let the lines PQ and RS be the two parallel tangents to circle at M and N respectively. Through centre O, draw line AB || line RS. OM = ON =... 1
- Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON. Proof: In ∆OMR and ∆ONR, seg RM ≅ seg RN [Tangent segment theorem] seg OM ≅ seg ON [Radii of the same circle] seg OR ≅ seg OR [Common side]... 1
- In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments seg RM and seg RN are tangents to the circle with centre O. [Given] ∴ ∠OMR = ∠ONR = 90° [Tangent theorem] i. In ∆OMR, ∠OMR = 90° ∴ OR2 = OM2... 1
- In the adjoining figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A. i. line AB is the tangent to the circle with centre C and radius AC. [Given] ∴ ∠CAB = 90° (i) [Tangent theorem] ii. seg CA ⊥ line AB [From (... 2
- Seg AM is a median of ∆ABC. If AB = 22, AC = 34, BC = 24, find AM. ∴ AM = 26 units 1
- Find the length of a diagonal of a rectangle having sides 11 cm and 60 cm. Answer: 61 cm A diagonal divides the rectangle into two right-angled triangles, with the sides of the rectangle as the legs and the diagonal... 1
- Do sides 7 cm, 24 cm, 25 cm form a right angled triangle? Give reason. The sides of the triangle are 7 cm, 24 cm and 25 cm. The longest side of the triangle is 25 cm. ∴ (25)² = 625 Now, sum of the squares of the... 1
- Find the height of an equilateral triangle having side 2a. Let ∆ABC be the given equilateral triangle. ∴ ∠B = 60° [Angle of an equilateral triangle] Let AD ⊥BC, B – D – C. In ∆ABD, ∠B = 60°, ∠ADB = 9... 1
- In the figure 7.12, a cylindrical wrapper of flat tablets is shown. The radius of a tablet is 7 mm and its thickness is 5 mm. Radius of a tablet, r = 7 mm Thickness of a tablet, h = 5 mm Radius of cylindrical wrapper, R = 14/2 = 7 mm Height of wrapper (H) = 10 cm =... 1
- In figure 7.11, a toy made from a hemisphere, a cylinder and a cone is shown. Find the total area of the toy Radius of the sphere = Radius of the cylinder = Radius of cone = r = 3 cm Height of the cone, h = 4 cm Height of the cylinder, H = 40 cm Let... 1
- A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm2 . Height of the cylinder, h = 3 cm Let the radius of the cylinder be r cm and the height of the cone be H cm. Area of the base of cylinder = 1... 1
- Observe the measures of pots in figure 7.8 and 7.9. How many jugs of water can the cylindrical pot hold ? Given: For the conical water jug, radius (r) = 3.5 cm, height (h) = 10 cm For the cylindrical water pot, radius (R) = 7 cm, height (H) = 10... 2
- The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base Radius is 21 cm 1
- Find the surface area of a sphere of radius 7 cm. Answer is 616 sq. cm 1
- Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm. Given :: radius of base of cylinder= 5 cm height = 40 cm for cylinder , Total surface area of cylinder = 2π r (r+h) =2x3.14x5x(5+40) =2x3.14... 1
- Find the volume of a sphere of diameter 6 cm For the sphere , diameter d=6 cm radius r= diameter/2 = 6/2 =3 Volume of sphere = 4/3π r³ = 4/33.14 x 3³ =113.04 cm³ 1
- Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm. The correct Answer is 11.79 cm³ =11.79 cm³ 1
- A kite is flying at a height of 60 m above the ground. The string attached to the kite is tied at the ground. It makes an angle of 60° with the ground. Given data: Height of kite above the ground: 60 m Angle between the string and the ground: 60° Formula used: sine function: sin(angle) = opp... 1
- A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60° with the horizontal. Find the height of the tree. Correct Answer is 40+20√3 m 1
- Two poles of heights 18 metre and 7 metre are erected on a ground. The length of the wire fastened at their tops in 22 metre Correct answer is 30 degree 1
- Two buildings are facing each other on a road of width 12 metre. From the top of the first building, which is 10 metre high, the angle of elevation See image for answer 2
- From the top of a lighthouse, an observer looking at a ship makes angle of depression of 60°. If the height of the lighthouse is 90 metre Correct Answer is 51.9 m 1