Questions Archive - Page 129 Of 158

Question

The height of a right circular cone is twice the radius of the base. If the height were seven times the diameter of the base then the volume of the cone would have been 539 cu cm more. Find the height of the cone.

The height of a right circular cone is twice the radius of the base. If the height were seven times the diameter…

30/09/2025

Question

Two solid spheres with radii of 1 cm and 6 cm lengths are melted and a hollow sphere with an outer radius of 9 cm is made. Determine the inner radius of the new hollow sphere.

Two solid spheres with radii of 1 cm and 6 cm lengths are melted and a hollow sphere with an outer radius…

30/09/2025

Question

From the roof of the building the angle of depression of the top and foot of the lamp post is 30° and 60° respectively. Find the ratio of the heights of the building and the lamp post.

From the roof of the building the angle of depression of the top and foot of the lamp post is 30° and…

30/09/2025

Question

Angle of elevation of the top of an incomplete tower from a point at a distance 50 m from its foot is 30°. How much should the height of the tower be increased so that the angle of elevation of the top will be 45° from that point?

Angle of elevation of the top of an incomplete tower from a point at a distance 50 m from its foot is…

30/09/2025

Question

Show that (tan θ + sec θ – 1) / (tan θ – sec θ + 1) = (1 + sin θ) / cos θ

Show that =

30/09/2025

Question

Radius of a circle is 7 cm. Find the angle in radians which is subtended by an arc of this circle of length 5.5 cm at the centre of the circle.

Radius of a circle is 7 cm. Find the angle in radians which is subtended by an arc of this circle of…

30/09/2025

Question

If cos θ = [katex]\frac{x}{\sqrt{x²+y²}}[/katex] , then prove that x sin θ = y cos θ

If cos θ = , then prove that x sin θ = y cos θ

30/09/2025

Question

Construct a square of the equal area of an equilateral triangle of side 7 cm.

30/09/2025

Question

Draw a right-angled triangle of which two sides containing the right angle have the lengths 5 cm and 6 cm. Now draw an incircle of the triangle.

Draw a right-angled triangle of which two sides containing the right angle have the lengths 5 cm and 6 cm. Now draw…

30/09/2025

Question

Prove that a cyclic trapezium is an isosceles trapezium.

30/09/2025

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The height of a right circular cone is twice the radius of the base. If the height were seven times the diameter of the base then the volume of the cone would have been 539 cu cm more. Find the height of the cone.

Two solid spheres with radii of 1 cm and 6 cm lengths are melted and a hollow sphere with an outer radius of 9 cm is made. Determine the inner radius of the new hollow sphere.

From the roof of the building the angle of depression of the top and foot of the lamp post is 30° and 60° respectively. Find the ratio of the heights of the building and the lamp post.

Angle of elevation of the top of an incomplete tower from a point at a distance 50 m from its foot is 30°. How much should the height of the tower be increased so that the angle of elevation of the top will be 45° from that point?

Show that (tan θ + sec θ – 1) / (tan θ – sec θ + 1) = (1 + sin θ) / cos θ

Radius of a circle is 7 cm. Find the angle in radians which is subtended by an arc of this circle of length 5.5 cm at the centre of the circle.

If cos θ = [katex]\frac{x}{\sqrt{x²+y²}}[/katex] , then prove that x sin θ = y cos θ

Construct a square of the equal area of an equilateral triangle of side 7 cm.

Draw a right-angled triangle of which two sides containing the right angle have the lengths 5 cm and 6 cm. Now draw an incircle of the triangle.

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