Volume and Surface Area Questions

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
If S is sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?

PQRS is a square, M is the mid-point of PQ and N is a point on QR such that NR is two-third of QR. If the area of ΔMQN is 48 cm2 , then what is the length (in cm) of PR ?

ΔABC a right angled triangle has ∠B = 90° and AC is hypotenuse. D is its circumcentre and AB = 3 cms, BC = 4 cms. The value of BD is

A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area ?

Three consecutive angles of a cycle quadrilateral are in the ratio of 1 : 4 : 5 . The measure of fourth angle is

A solid cone of height 24 cm and radius of its base 8 cm is melted to form a solid cylinder of radius 6 cm and height 6 cm. In the whole process what
percent of material is wasted?

In the given figure, PQR is an equilateral triangle with side as 12 cm. S and T are the mid points of the sides PQ and PR respectively. What is the area (in sq.cm) of the shaded region?

In the given figure, ABC is a right angled triangle. ABC = 90 deg and ACB = 60 deg. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle?