How many spherical balls of radius 1 cm can be made by melting a hemisphere of radius 6 cm?1). 1122). 1083). 1164). 104
Let be the number of spherical balls that can be made
So, we have
⇒ 2/3(π)(6)3 = n × 4/3(π)(1)3
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1. If $V_{1}$, $V_{2}$,$V_{3}$ be the volumes of a right circular cone, a sphere and a right circular cylinder having the same radius and same height, then
2. Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle, thus formed, with that of the original triangle is.
3. The perimeter of a square is twice the perimeter of rectangle. If the perimeter of the square is 72 cm and the length of the rectangle is 12 cm, what is the difference between the breadth of the rectangle and the side of the square?
4. A right angled sector of radius r cm is rolled up into a cone in such a way that the two binding radii are joined together. Then the curved surface area of the cone is
5. A rectangular swimming pool of length 25 m and breadth 12 m has a uniformly sloping floor. It is 2 m in depth on one end of its length and 3 m at the other. How much water is needed to completely fill this pool?
6. If the perimeter of a semicircula field is 144m, then the diameter of the field is (Take $\pi$ = $\frac{22}{7}$)
7. The base of a right circular cone has the same radius a as that of a sphere.Both the sphere and the cone have the same volume.Height of the cone is
8. $\triangle$ABC is similar to $\triangle$PQR. Length of AB is 18 cm and length of the corresponding side PQ is 12 cm. If area of $\triangle$ABC is 324 sq cm, what is the area of $\triangle$PQR?
9. What is the area of the sector whose central angle is 90° and radius of the circle is 14 cm?
10. In $\triangle ABC$, a line through A cuts the side BC at D such that BD : DC = 4:5. If the area of $\triangle ABD$ = 60 sq.cm., then the area of $\triangle ADC$ is
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