A class VII teacher wants to discuss the following problem in the class. "A square is divided into four congruent rectangles. The perimeter of each rectangle is 40 units. What is the perimeter of given square?" Key mathematical concepts required to solve this problem is

• area of square and rectangle, perimeter of square and rectangle and definition of square and rectangle

• meaning of the terms square, rectangle, congruent, perimeter etc

• area of rectangle, perimeter of squa

• formation of algebraic equation to solve the problem

Identify the open-ended problem.

(1) Parikshit makes a cuboid of dimensions 5 cm, 2 cm and 5 cm. How many such minimum cuboids are required to form a cube?

(2) Find the cube-root of 512 using prime factorization method

(3) Find the cube of 10

(4) Write any 5 numbers whose cube is more than 64

If the area of an equilateral triangle is 16$\sqrt{3}$ cm, then the perimeter of the triangle is

• 48cm

• 24cm

• 12cm

• 36cm

A vessel is in the form of an open inverted cone of height 8 cm and radius of its top is 5 cm. It is filled with water upto the brim. When lead shots are dropped into the vessel, one fourth of the water flows out. The number oflead shots dropped in the vessel where radius of each lead shot is 0.5 cm

• 50

• 75

• 100

• 150

OA, OB and OC are edges of a cube meeting at vertex O. If length of each is a cm, then area of $∆$ABC will be

• a² cm²

• $\frac{\sqrt{3}}{4}{\mathrm{a}}^2 {\mathrm{cm}}^2$

• $\frac{\sqrt{3}}{2}{\mathrm{a}}^2 {\mathrm{cm}}^2$

• $\frac{3}{4}\mathrm{a} {\mathrm{cm}}^2$

Two cylinders have equal volumes and their heights are in the ratio 1: 3. The ratio of their radii will be

• 1 : 3

• 3 : 1

• $\sqrt{3} :\hspace{0.17em}3$

• $3 : \sqrt{3}$

Area of two similar triangles are 4 cm² and 9 cm² respectively. The ratio of their corresponding sides is

• 4 : 9

• 9 : 4

• 3 : 2

• 2 : 3

A cuboid is of dimensions 5 cm x 2 cm x 5 cm. How many such cuboids may be joined to form a cube ?

• 32

• 16

• 25

• 20

In a right triangle, the square of hypotenuse is equal to twice the product of remaining two sides. If the base of this triangle is 12 cm, then the perpendicular of triangle will be

• 12cm

• 10/2cm

• 9cm

• 6cm

The radii of the bases of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5: 3. The ratio of their volumes is

• 7 : 6

• 10 : 9

• 4 : 9

• 20 : 27