The shape of a pencil with one end sharpened is the combination of a and a _____.

The radius of a right circular cylinder and a hemisphere is equal and their volumes are also equal. The height of the hemisphere is greater than the height of the cylinder by (a) 25% (b) 50% (c) 100% (d) 200%

The lower part of an ice-cream is conical and upper part is hemispheric with same circular base. If the height of the cone is 9cm and radius of the base 2.5 cm. Find the volume of the ice-cream.

If the height and base area of a solid hemisphere and a solid cylinder are same, then the ratio of their volume is (a) 1 : 3 (b) 1 : 2 (c) 2 : 3 (d) 3 : 4

Find the mean proportion of xy² and xz²

The ratio of portion of profit of two friends is 1/2 : 1/3. Find the ratio of their capitals

If x be the number of edges of a parallelepiped and y be the number of surfaces then for what least value of a, (x + y + a) is a perfect square?

If sin (θ + 30°) = cos 15°, then find the value of cos 2θ.

From an external point P of a circle with centre O, two tangents PS and PT are drawn. QS is a chord of the circle parallel to PT. If ∠SPT = 80°, then find the value of ∠QST.

Perimeters of two similar triangles are 27 cm and 16 cm. If the length of a side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle

If x ∝ √y and y = a², when x = 2a then find x² : y

If x\over2 = y\over3 = z\over4 then find the value of (3x + 4y + 8z) / (x + 3y).