Mensuration Test 5

 A conical tent has the capacity to accommodate 10 persons with per person, 6 m² space to sit and 30 m³ of the air to breath. How high the cone should be so that these persons could stay comfortably?

 Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is 14 cm, then the remaining area enclosed between the circumference of the circles inside the square is:

 In the middle of a circular park of radius 2r units, a circular hole of radius r units has been dug. The mud extracted from the hole has been spread uniformly over one third of the rest of the park, to make an elevated platform around the hole. This has led to an increase of 5 units in initial depth of the hole. Find the percentage increase in depth of the hole.

 The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 10 cm and the breadth is less than the length of the side of the square by 5 cm. the perimeter of the rectangle is :

In the following question, two statements are numbered as Statement I and II. On solving these statements we get Quantity A and B respectively. Solve the given statements for the both quantities and choose the correct option.

Statement I: The sides of a rectangular plot are in the ratio 1 : 4. If the cost of mowing the plot is Rs. 500 at the rate of Rs. 3.2/m², find the perimeter of the plot.Statement II: The cost of fencing a square lawn is Rs. 630 at the rate of Rs. 11.2/m. If the sides of the plot are in the ratio 4 : 5, then find the length of the largest side of the square lawn.

Directions For Questions

Directions: In the given figure, a square shape land ABCD is enclosed in a circular land and Q1 and Q2 are two areas of the fields in triangular shaped land BCE.

Two horses are tied up at point A and C with tight rope and are allowed to gaze

7. Directions For Questions

Directions: In the given figure, a square shape land ABCD is enclosed in a circular land and Q1 and Q2 are two areas of the fields in triangular shaped land BCE.

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option.

Quantity A: Find the curved surface area of a cone with radius 3.5 cm and height 6 cm.Quantity B: Find the total surface area of a cone with radius 2.1 cm and height 4 cm.

A spherical shaped sweet is placed inside a cube of side 5 cm such that the sweet just fits the cube. A fly is sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet?

An oil funnel made of tin sheet consist of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make a funnel.

Quantity A: Perimeter of a rectangle is 70 cms and the length and the breadth are in the ratio of 4 : 3 respectively. What is the area of rectangle in square cm?Quantity B: A conical tent is made of canvas whose height is 13 cm and radius is 7 cm. The canvas required is

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Quantity A: The perimeter of one face of a cube is 23 cm. Then its volume (in cm³):Quantity B: The volume of a cube is 4096 m³. The total length of all its edges (in m):

A rectangle water reservoir is 12 metres long and 6 metres wide at base. Water flows into it at the rate of 10 m per sec. through the pipe having the cross section 9 cm × 3 cm. Then the height to which the water will rise in the reservoir in 20 minutes is :

A cylindrical bucket of height 36 cm and radius 21 cm is filled with fine iron ore. The bucket is emptied on the ground and a conical heap of fine iron ore is formed, the height of the heap being 12 cm. The radius of the heap at the base is:

Rohan got a toy on his birthday, which is a bubble stick that is in the shape of a right circular cylinder with hemispherical ends. The total length of the toy is 25cm. The diameter of the cylinder is ¼ of its height. Find its surface area. (Take π= 22/7)