Question

1.A toy is made with seven equal cubes of sides √7cm.Six cubes are joined to six faces of a seventh cube. Find the total surface area of the toy.
2.A point P is 25 cm from the center O of the circle. The length of the tangent drawn from P to the circle is 24 cm .Find the radius of the circle .

Answer 1

Answer:

1.) 210 sq. cm. 2.) 7 cm

Step-by-step explanation:

1.) The formula for the Total Surfae Area is given by

$TSA=6 \times 5 \times s \times s$

because there are 6 cubes and 5 faces per cube.

Substituting $s=\sqrt{7}$, we get

TSA=210 sq. cm.

2.) Any tangent line segment to a circle is perpendicular to a radius towards the point of tangency Q.  So the line segment OP, the radius r and PQ forms a right triangle where OQP is the right angle.

Using pythagorean theorem,

$OP^2=r^2+QP^2$

Subsituting OP=25 and QP=24, we get

$r=\sqrt{25^2-24^2}=7$

We have r=7 cm

Answer 2

Answer:

210 sq cm, 7 cm

Step-by-step explanation:

1. We know surface area of a cube = 6 a^2 = 6 x 7 = 42 sq cm

So 5 faces of 6 cubes are obtained when 6 cubes are combined to 6 faces of 7th cube.

So total surface area will be 6 x 5 x a^2

                               = 30 x (√7)^2

                             = 30 x 7

                            = 210 sq cm

2. Draw a circle. Let B be a point. So that OB = 25 cm.

Let AB be a tangent to the circle so that AB = 24 cm.

Join OA. OA is the radius.

OA is perpendicular to BA

In right angled triangle OAB, we get (by applying pythagoras theorem

OB^2 = OA^2 + AB^2

OA^2 = OB^2 – AB^2

OA^2 = 25^2 – 24^2  

        = 625 – 576

OA^2   = 49  

OA = √49

OA = 7 cm

So length of radius is 7 cm