SSC (Marathi Semi-English) इयत्ता १० वी - Maharashtra State Board Important Questions for Geometry Mathematics 2

Draw the circumcircle of Δ PMT in which PM = 5.4, P = 60°, M = 70°.

A circle is inscribed in square ABCD of side 14 cm. Complete the following activity to find the area of the shaded portion.
  Activity:

Area of square ABCD = ______

= 14²  
 = 196 cm² 
Area of circle = πr²     = `22/7xx 7^2`   
= ____ cm²

Area of shaded portion = Area of square ABCD – Area of circle   

 = 196 – _______

= _____ cm²

In the given figure `square`ABCD is a square of side 50 m. Points P, Q, R, S are midpoints of side AB, side BC, side CD, side AD respectively. Find area of shaded region

If x = `θ/360` × 2πr then what is x in the formula?

In the figure, PQRS is a square with side 10 cm. The sectors drawn with P and R as centres form the shaded figure. Find the area of the shaded figure. (Use π = 3.14)

In the given figure, a rectangle ABCD is inscribed inside a semi-circle of radius 10 cm. Using the dimensions given in the figure, determine the area of the shaded region.

A milk container of height 16 cm is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.

The perimeter of an arc of radius 4.2 cm is 12.8 cm. Determine the angle subtended by the arc at the centre of circle.

Find the total surface area of frustum, if its radii are 15 cm and 7 cm. Also, the slant height of the frustum is 14 cm.

Radii of the frustum = `square` cm and `square` cm

Slant height of the frustum = `square` cm

Total surface area = `π[(r_1^2 + r_2^2 + (r_1 + r_2)l]`

= `22/7 [square + square + (square + square) square]`

= `22/7 (square)`

= `square` cm²

Hence, the total surface area of the frustum is `square`.

If radius of the base of cone is 7 cm and height is 24 cm, then find its slant height.

In the figure given above, `square`ABCD is a square and a circle is inscribed in it. All sides of a square touch the circle. If AB = 14 cm, find the area of shaded region.

Solution:

Area of square = `(square)^2`   ......(Formula)

= 14²

= `square  "cm"^2`

Area of circle = `square`    ......(Formula)

= `22/7 xx 7 xx 7`

= 154 cm²

(Area of shaded portion) = (Area of square) - (Area of circle)

= 196 − 154

= `square  "cm"^2`