Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Surface Areas and Volumes

Short Answer Type

451. A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

3173 Views

452. If the surface are as of two spheres are in the ratio 4 : 9, then find the ratio of their volumes.

1702 Views

453. If two cones have their volumes in the ratio 3 :1 and their heights are in the ratio 1 : 3, then find the ratio of their radius.

Let the radii be r₁ and r₂ and heights be h₁ and h₁ Then

straight V subscript 1 over straight V subscript 2 equals fraction numerator begin display style 1 third end style πr subscript 1 squared straight h subscript 1 over denominator begin display style 1 third end style πr subscript 2 squared straight h subscript 2 end fraction equals open parentheses r subscript 1 over r subscript 2 close parentheses squared space x space open parentheses h subscript 1 over h subscript 2 close parentheses rightwards double arrow space 3 over 1 equals open parentheses r subscript 1 over r subscript 2 close parentheses squared cross times open parentheses 1 third close parentheses rightwards double arrow open parentheses 3 over 1 close parentheses squared equals open parentheses r subscript 1 over r subscript 2 close parentheses squared rightwards double arrow space space space r subscript 1 over r subscript 2 equals 3 over 1

Thus, the ratio of their radius is 3 :1.

152 Views

454. The radius of a solid hemispherical toy is 3.5 cm. Find the total surface area.

124 Views

455. If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume, what is the diameter of the sphere?

133 Views

456. Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

791 Views

457. A cylinder and a cone are of the same base radius and of same height. Find the ratio of the volume of cylinder to that of the cone.

2464 Views

458. A right circular cylinder and a right circular cone have the same base radius and same height. What is the ratio of the volume of the cylinder to that of cone?

156 Views

459. Find the maximum volume of a cube that can be carved out of a solid hemisphere of radius r.

456 Views

460. A glass cylidner with diameter 20 cm has water to a height of 9 cm. A metal cube at 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder.

148 Views