Questions & Answers: "Geometry (Angles, Circles, and 3D Nets)"

All the vertices of a triangle are on the circumference of the circle at equal distances from each other and at a distance of 14 cm. from the centre of the circle. What will be the length of the median of that triangle?

Two triangles are formed by diagonal BD of kite ABCD as shown in the figure. Which test from the following is not applicable for proving these two triangles are congruent?

In the adjoining circle with center C, m∠PRS = 55°; then m∠PSQ = ?

In the adjoining figure, line AB || line CD and m∠RGC = 50°, then find m∠SFA - m∠PEA = ?

Length of the longest chord of a circle is 7 m. What will be the length of the parallel chord to it, at a distance of 2.1 m.?

‘Diagonals of the are perpendicular bisectors of each other.’ Choose the correct alternative from given options to complete the above statement. (A) Rectangle (B) Square (C) Rhombus (D) Parallelogram (E) Kite

Observe the two planes X and Y shown in the diagram and select ‘two correct’ statements from given.

In the adjoining figure of ΔEFG, point H is the mid-point of the seg FG. If m∠EFH = 45° and l(EF) = l(EG) = 10 2 cm., then l(EH) = ? cm.

The sides forming right angle of a right-angled triangle are 7 cm and 24 cm. Find the radius of the circumcircle of the triangle.

The diameter of a ball is 20 cm. Find the volume of the air in the ball. (π = 3.14)

The inner surface of a cylindrical well of height 14m and radius 250 cm is to be plastered with cement-sand layer. At the rate of Rs. 100 per square meter, what will be the total cost in rupees?

In the adjoining figure ∠y = 90°, l(xy) = 8m. l(yz) = 15m, WM ⊥ XZ, WM = 6m. Find the area of the figure.

Two lines are intersecting each other. The measures of the vertically opposite angles in a pair are (2x + 65)° and (7x – 10)°. Find the measures of each remaining angle.

AC is the diameter of a circle. ‘B’ is any point on the circle. Find the false statement from the following. (Choose two correct options)

Two rectangular grounds have area 1541 sq. m. and 759 sq. m. respectively. If both the grounds have same breadth, find the breadth of the ground.

Where is the ortho center of a right-angled triangle located?

In the adjoining figure ∠TPQ ≅ ∠TPR. Side PQ ≅ side PR. Then by which test Δ QPT and Δ RPT are congruent?

The measure of an angle is 1/5 times the measure of its supplementary angle. Find the measure of its complementary angle.

Observe the following figure and select the correct statements. (A) Line AB and line BA are different lines. (B) Line AB and line DC intersect at ‘O’. (C) Point C, O and B are noncollinear points.

Find the capacity of a hollow cube whose side is 10 cm. (Choose two correct options)

Area of a circle is denoted by ‘A’ and radius by ‘r’. Choose the correct statement from the following that states the correct relation of variation between A and r.

If the ratio of the measures of angles of ☐ABCD taken in order is 7:8:4:5. Find the type of ☐ABCD.

Which of the following can be the measure of an angle in the minor segment?

There is a regular hexagon having each side 14 cm. On every side a semicircle is drawn from outside the hexagon, taking each side as the diameter. Find the perimeter of the figure so formed.

In the adjoining figure, an isosceles trapezium is drawn. The measurements of sides of the figure are as follows. l(QR) = l(PS) = 5 units, l(PQ) = 5 units, l(PT) = 4 units. Find the area of ☐PQRS.

The ratio of supplementary angle and complementary angle of a given angle is 8:3. Then what will be the ratio of given angle with its supplementary angle?

What is the cost of fencing a circular garden of radius 28 m with five rounds of wire, if the wire costs Rs. 50 per m?

Which of the following statement is not true? (Choose two correct options) (A) The opposite angles of a parallelogram are congruent. (B) The adjacent sides of a parallelogram are congruent. (C) The diagonals of a parallelogram are congruent. (D) The diagonals of a parallelogram bisect each other.

The length of a cuboidal tank is one and half time its breadth and height is twice the length. If volume of the tank is 4500 cubic meter, then what is the height of tank? (Choose two correct options)

If the diameter of a wheel of a tractor is 1.4 m. then how much distance is covered by the wheel in 400 complete rotations.

In the following fig. line l || line m || line n and line x and line y are their transversals. If AB = 18 cm, BC = 30 cm, QR = 21 cm then PR = ?

Two angles of measure 40º and 140º with different vertex are drawn then which of the following statement is true?

The co-ordinate of point P on a number line is – 3/7. The distance between point P and point Q is 2 units then what will be the co-ordinate of point Q? (Choose two correct options)

The radius of a circle with center 'O' is 10 cm. The length of a chord is 16 cm. Find the distance of the chord from the center of the circle.

A hall has length 30 meter and breadth 9.5 m. For flooring this hall, the square tiles are to be used of half meter side then how many tiles should be required?

The sides forming right angle of a right-angled triangle are 8 cm and 15 cm then what is radius of circumcircle of that triangle?

If the side of an equilateral triangle is 18 cm, then what is its area?

A rope of length 216 m. is cut at five places at same distance then what is the length of each piece in cm?

The curved surface area of a cone is 47.10 sq.cm. If radius of the base is 3 cm then what is its perpendicular height? (p =3.14 cm)

How many coins of thickness 0.2 cm and diameter 4 cm will be formed by melting a solid metallic cuboid of length 22 cm, breadth 18 cm and height 6 cm?

The area of a square is 4.41 sq.cm., then what is its perimeter?

The base radius of a cylindrical tank is 28 cm. It contains water. A metal cuboid of length 44 cm, breadth 14 cm and height 8 cm is dropped into it. Then what is the increase in the level of water in tank?

The length of side of a rhombus is 17 cm. If the length of one diagonal is 16 cm then what is the length of other diagonal?

The measures of exterior angles of a triangle are 115º and 117º respectively, then which type of triangle is it?

The length of a diagonal of a square is 11 cm then what is the length of its side?

The measure of a minor arc is 160° then what is the measure of corresponding major arc?

In a circle, the measure of a major arc is 60° more than double the measure of its minor arc. What will be the measure of its major arc?

Which of the following options indicate the volume of a sphere?

If a supplementary angle of an angle’s complementary angle is 108°, find the measure of the angle.

In the adjoining figure, the diagonal of a square is 12 cm. Find the length of every side.

Four vertices of a square lie on the circle as shown in the figure. The center of the circle is ‘O’ and radius is 7cm. Find the area of the shaded portion.

In the adjoining figure, l, m, n are parallel lines. m ∠ DAO = 60° m ∠ OCE = 35°, then m ∠ AOC = ?

Which of the options given below are incorrect statements? (Select two correct alternatives) (A) A ray has a midpoint. (B) A line has a midpoint. (C) Chord of a circle has a midpoint. (D) Perpendicular bisector of a line segment passes through its midpoint.

By which of tests, Δ ABC and Δ DCB from the given figure will be congruent?

□ ABCD is a cyclic quadrilateral. Point E lies on the ray BC as B – C – E. If m ∠ DCE = 95°, then m ∠ DAB = ?

From a rectangular thermocol sheet with dimension 20 cm × 10 cm, a rectangular piece of 2 cm × 5 cm dimension is cut. Which of the following sentences will be correct for the thermocol sheet?

In the figure, line l and m intersect in point O. Find the value of ‘y’.

Which of the following conditions should be given to make the total surface area of a sphere and cylinder to be equal?

Which of the following options is not a pythagorean triplet?

What is the product of two integers between which -(119/13) lie?

The length, breadth and height of a cuboid is ‘l’ cm ‘b’ cm, ‘h’ cm. If l b = 60 sq. cm, bh = 24 sq. cm, hl = 40 sq. cm, then find the volume of cuboid.

A semicircle is drawn over a diameter. The circumference of the semicircle is 72 units. l(BC) = l(AO) = l(OC). Find the perimeter of Δ ABC.

Which of the following options is the co-efficient form of the polynomial

In Δ PQR, angle bisectors of ∠ Q and ∠ R intersect at point O. m ∠ O = 130°, m ∠ P = ?

If a transversal intersects two parallel lines, then find the ratio of the number of pairs of alternate angles to the number of pairs of corresponding angles so formed.

Find the ratio of the total surface area of the hemisphere with diameter 28 cm to surface area of a sphere having radius 14 cm.

The measure of a given angle is 1/4 times that of its supplementary angle. Find the measure of its complementary angle.

Find the measure of the angle between the hour hand and minute hand of a clock at 15 minutes past 2.

The diagonal of a square is 25√2 cm. Find the area of the square.

How much less is the area of a square whose perimeter is 44 cm. than the area of a circle whose circumference is 44 cm.

A bus has wheels of diameter 1.4m. Travelling from one town to other, the wheels complete 20,000 rotations. Find the distance covered by the bus. [Select two correct alternatives]

How much water will a cylindrical tank contain if its height is 10 m and diameter is 14m.

The diagonals of a rhombus are 24 cm and 32 cm. Find the perimeter of the rhombus.

A cuboid box has length 60 cm breadth 18 cm and height 15 cm. How many cubical boxes having each side 6 cm. will be contained in the box.

Observe the given figure and find the odd term.

The perimeter of a semi-circular garden is 180 m. Find the area of the garden.

A pit 60 m long, 40 m wide and 5 m deep was dug and the soil was spread evenly over a road of length 1 km. and breadth 24 m. What was the thickness of the soil spread?

The sides forming the right angle of a right-angled triangle are 5 cm. and 12 cm. Find the radius of the circumcircle of the triangle

Total surface area of a cube is 384cm². Find the volume of that cube.

Solve.

Find the perpendicular height of an equilateral triangle whose side is 12 cm.

In the above trapezium PQRS side PQ 11 side SR. The measurements of the sides are given in the figure. observe the figure and find the area of the trapezium.

The area of an equilateral triangle is $100 \\sqrt{3}$ sq.cm. Find the perimeter of that equilateral triangle.

The difference between half circumference of a circle and its diameter is 4 cm. Find the area of the circle.

In the adjoining figure line $l||$ line $m$ and line $p$ is the transversal. Observe the figure and find the value of $\angle w$.

How many more segments are formed by joining six collinear points to each other than by joining five non-collinear points to each other?

In the adjoining $\triangle PQR$, ray PA and ray QB are the bisectors of $\angle P$ and $\angle Q$ respectively. If $\angle R=70^\circ$. Find $m \angle PMQ$.

In the adjoining $\triangle PQR$, $\angle AQP=130^\circ$, $\angle BRP=140^\circ$, $l(PQ)=16$ cm, $l(PR)=12$ cm. Find $l(QR)$.

Opposite angles of a cyclic quadrilateral are $(3x+10)^\circ$ and $(4x+30)^\circ$. Find the measures of these angles.

In the adjoining $\triangle PQR$, $\angle PQR=90^\circ$ and $QM \perp PR$, $PQ=12$ cm, $QR=16$ cm. Find $l(QM)$.

In the adjoining figure PQRS is a square having side 28 cm. Points A, B, C and D are the midpoints of side PQ, side QR, side RS, side SP respectively. Find the area of square ABCD.